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<title>Přijímací zkoušky z matematiky - online testování | ČVUT FSv - K101 Matematika</title>
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</a>
<p style="padding: 0.5em;"><strong><a href="http://intranet.cvut.cz/cs?set_language=cs" title="ČVUT">ČVUT</a> <a href="http://www.fsv.cvut.cz/hlavni.php" title="Fakulta stavební">FSv</a></strong>
– <strong><a href="https://mat.fsv.cvut.cz/" title="Katedra matematiky">
Katedra matematiky</a></strong><br />
Thákurova 7, 166 29 Praha 6<br />
Tel.: <a href="tel:+420224354390"><strong>+420 / 224 354 390</strong></a>
</p>
</div>
<div id="eu">
<img src="/entrance/images/opvvv.jpg" /><br />
<table>
<tr><td>Příjemce:</td><td>České vysoké učení technické v Praze</td></tr>
<tr><td>Registrační číslo projektu:</td><td>CZ.02.2.69/0.0/0.0/16_015/0002382</td></tr>
<tr><td>Název projektu dle MS2014+:</td><td>Institucionální podpora Českého vysokého učení technického v Praze</td></tr>
</table>
</div>
<h2>Přijímací zkoušky z matematiky – online testování</h2>
<div id="zbyvacas" class="zbyvac1"></div>
<form method="post" accept-charset="utf-8" action="/entrance/oprav/3a52ed1ad87c2e09e7a66a3e0d06de08">
<p>V následujícím online testu se na každou z 15 otázek nabízí 5 odpovědí, ale vždy <strong>jen jedna</strong> je správná.</p>
<p>Výsledek, který považujete za správný, <strong>označte v obrazci vlevo</strong>.</p>
<p>Označování odpovědí funguje ve všech prohlížečích, které podporují CSS pseudo třídu <code>:checked</code>. Pokud se Vám odpovědi neoznačují, přestože jste je vybrali, zkuste jiný prohlížeč. I pokud se Vám odpovědi neoznačují, přestože jste je vybrali, jsou vybrané a zpracují se po odeslání testu k vyhodnocení.</p>
<p>Doba vymezená na provedení testu je <strong>70 minut</strong>. Po uplynutí této doby testu je test ukončen a vyhodnocen. Test lze ukončit před uplynutím této doby. Zbývající doba je zobrazena v pravém horním rohu.</p>
<p id="java" class="cerveny">Pro správnou funkci je zapotřebí mít povolený javascript.</p>
<table class="test">
<tr>
<td>
<table class="odpovedi">
<tr>
<td class="licha jednoducha"><input name="1" id="odp1a" type="radio" value="1" /><label for="odp1a">a</label></td>
<td> </td>
<td class="licha jednoducha"><input name="1" id="odp1b" type="radio" value="2" /><label for="odp1b">b</label></td>
</tr>
<tr>
<td> </td>
<td class="licha jednoducha"><input name="1" id="odp1c" type="radio" value="3" /><label for="odp1c">c</label></td>
<td> </td>
</tr>
<tr>
<td class="licha jednoducha"><input name="1" id="odp1d" type="radio" value="4" /><label for="odp1d">d</label></td>
<td> </td>
<td class="licha jednoducha"><input name="1" id="odp1e" type="radio" value="5" /><label for="odp1e">e</label></td>
</tr>
</table>
1 bod
</td>
<td>
<table class="otazky">
<tr><td>1. Přímky ${(a-2)x+(2b+1)y-1=0}$ a ${ax+(2-3b)y+3=0}$ jsou totožné právě tehdy, když</td></tr>
<tr><td><label for="odp1a">a) $a=\frac32\lland b=-\frac53$</label></td></tr>
<tr><td><label for="odp1b">b) $a=-5\lland b=8$</label></td></tr>
<tr><td><label for="odp1c">c) $a=1\lland b=3$</label></td></tr>
<tr><td><label for="odp1d">d) $a=3\lland b=-5$</label></td></tr>
<tr><td><label for="odp1e">e) $a=-1\lland b=-3$</label></td></tr>
</table>
</td>
</tr>
<tr>
<td>
<table class="odpovedi">
<tr>
<td class="licha dvojita"><input name="2" id="odp2a" type="radio" value="1" /><label for="odp2a">a</label></td>
<td> </td>
<td class="licha dvojita"><input name="2" id="odp2b" type="radio" value="2" /><label for="odp2b">b</label></td>
</tr>
<tr>
<td> </td>
<td class="licha dvojita"><input name="2" id="odp2c" type="radio" value="3" /><label for="odp2c">c</label></td>
<td> </td>
</tr>
<tr>
<td class="licha dvojita"><input name="2" id="odp2d" type="radio" value="4" /><label for="odp2d">d</label></td>
<td> </td>
<td class="licha dvojita"><input name="2" id="odp2e" type="radio" value="5" /><label for="odp2e">e</label></td>
</tr>
</table>
2 body
</td>
<td>
<table class="otazky">
<tr><td>2. Hyperbola o rovnici ${x^2+4x-3y^2+6y+28=0}$ má střed ${S}$ a velikosti poloos $a$, $b$, kde</td></tr>
<tr><td><label for="odp2a">a) ${S[-2,\,1]}$, ${a=3}$, ${b=3\sqrt3}$</label></td></tr>
<tr><td><label for="odp2b">b) ${S[2,\,-1]}$, ${a=3\sqrt3}$, ${b=3}$</label></td></tr>
<tr><td><label for="odp2c">c) ${S[-2,\,1]}$, ${a=\sqrt3}$, ${b=3}$</label></td></tr>
<tr><td><label for="odp2d">d) ${S[2,\,1]}$, ${a=3\sqrt3}$, ${b=3}$</label></td></tr>
<tr><td><label for="odp2e">e) ${S[4,\,6]}$, ${a=\sqrt7}$, ${b=\sqrt{\frac{14}3}}$</label></td></tr>
</table>
</td>
</tr>
<tr>
<td>
<table class="odpovedi">
<tr>
<td class="licha jednoducha"><input name="3" id="odp3a" type="radio" value="1" /><label for="odp3a">a</label></td>
<td> </td>
<td class="licha jednoducha"><input name="3" id="odp3b" type="radio" value="2" /><label for="odp3b">b</label></td>
</tr>
<tr>
<td> </td>
<td class="licha jednoducha"><input name="3" id="odp3c" type="radio" value="3" /><label for="odp3c">c</label></td>
<td> </td>
</tr>
<tr>
<td class="licha jednoducha"><input name="3" id="odp3d" type="radio" value="4" /><label for="odp3d">d</label></td>
<td> </td>
<td class="licha jednoducha"><input name="3" id="odp3e" type="radio" value="5" /><label for="odp3e">e</label></td>
</tr>
</table>
1 bod
</td>
<td>
<table class="otazky">
<tr><td>3. Mezi čísla $-1$ a $-81$ jsou vložena tři čísla tak, že spolu s danými čísly tvoří pět po sobě jdoucích členů geometrické posloupnosti. Prostřední z vložených čísel je</td></tr>
<tr><td><label for="odp3a">a) $3$</label></td></tr>
<tr><td><label for="odp3b">b) $27$</label></td></tr>
<tr><td><label for="odp3c">c) $-9$</label></td></tr>
<tr><td><label for="odp3d">d) $9$</label></td></tr>
<tr><td><label for="odp3e">e) $-3$</label></td></tr>
</table>
</td>
</tr>
<tr>
<td>
<table class="odpovedi">
<tr>
<td class="licha jednoducha"><input name="4" id="odp4a" type="radio" value="1" /><label for="odp4a">a</label></td>
<td> </td>
<td class="licha jednoducha"><input name="4" id="odp4b" type="radio" value="2" /><label for="odp4b">b</label></td>
</tr>
<tr>
<td> </td>
<td class="licha jednoducha"><input name="4" id="odp4c" type="radio" value="3" /><label for="odp4c">c</label></td>
<td> </td>
</tr>
<tr>
<td class="licha jednoducha"><input name="4" id="odp4d" type="radio" value="4" /><label for="odp4d">d</label></td>
<td> </td>
<td class="licha jednoducha"><input name="4" id="odp4e" type="radio" value="5" /><label for="odp4e">e</label></td>
</tr>
</table>
1 bod
</td>
<td>
<table class="otazky">
<tr><td>4. Jestliže ${\cotg\alpha=1}$, pak $\sin2\alpha$ se rovná číslu</td></tr>
<tr><td><label for="odp4a">a) $1$</label></td></tr>
<tr><td><label for="odp4b">b) $\frac{\sqrt2}2$</label></td></tr>
<tr><td><label for="odp4c">c) $\frac12$</label></td></tr>
<tr><td><label for="odp4d">d) $-1$</label></td></tr>
<tr><td><label for="odp4e">e) $0$</label></td></tr>
</table>
</td>
</tr>
<tr>
<td>
<table class="odpovedi">
<tr>
<td class="licha dvojita"><input name="5" id="odp5a" type="radio" value="1" /><label for="odp5a">a</label></td>
<td> </td>
<td class="licha dvojita"><input name="5" id="odp5b" type="radio" value="2" /><label for="odp5b">b</label></td>
</tr>
<tr>
<td> </td>
<td class="licha dvojita"><input name="5" id="odp5c" type="radio" value="3" /><label for="odp5c">c</label></td>
<td> </td>
</tr>
<tr>
<td class="licha dvojita"><input name="5" id="odp5d" type="radio" value="4" /><label for="odp5d">d</label></td>
<td> </td>
<td class="licha dvojita"><input name="5" id="odp5e" type="radio" value="5" /><label for="odp5e">e</label></td>
</tr>
</table>
2 body
</td>
<td>
<table class="otazky">
<tr><td>5. Střed koule o poloměru $r$ je vrcholem rotačního kužele, jehož podstava se koule dotýká. Jestliže jsou povrchy obou těles stejné, poloměr podstavy kužele je</td></tr>
<tr><td><label for="odp5a">a) ${3r}$</label></td></tr>
<tr><td><label for="odp5b">b) ${\dfrac{5r}3}$</label></td></tr>
<tr><td><label for="odp5c">c) ${\dfrac{3r}2\,}$</label></td></tr>
<tr><td><label for="odp5d">d) ${\dfrac{4r}3\,}$</label></td></tr>
<tr><td><label for="odp5e">e) ${4r}$</label></td></tr>
</table>
</td>
</tr>
<tr>
<td>
<table class="odpovedi">
<tr>
<td class="licha jednoducha"><input name="6" id="odp6a" type="radio" value="1" /><label for="odp6a">a</label></td>
<td> </td>
<td class="licha jednoducha"><input name="6" id="odp6b" type="radio" value="2" /><label for="odp6b">b</label></td>
</tr>
<tr>
<td> </td>
<td class="licha jednoducha"><input name="6" id="odp6c" type="radio" value="3" /><label for="odp6c">c</label></td>
<td> </td>
</tr>
<tr>
<td class="licha jednoducha"><input name="6" id="odp6d" type="radio" value="4" /><label for="odp6d">d</label></td>
<td> </td>
<td class="licha jednoducha"><input name="6" id="odp6e" type="radio" value="5" /><label for="odp6e">e</label></td>
</tr>
</table>
1 bod
</td>
<td>
<table class="otazky">
<tr><td>6. Množinou všech řešení nerovnice ${\dfrac3{|x+2|}>\dfrac12}$ s neznámou ${x\in\R}$ je</td></tr>
<tr><td><label for="odp6a">a) $(-2,\,4)$</label></td></tr>
<tr><td><label for="odp6b">b) $(-\infty,\,-2)\cup(-2,\,\infty)$</label></td></tr>
<tr><td><label for="odp6c">c) $(-8,\,-2)\cup(-2,\,4)$</label></td></tr>
<tr><td><label for="odp6d">d) $(0,\,4)$</label></td></tr>
<tr><td><label for="odp6e">e) $(1,\,\infty)$</label></td></tr>
</table>
</td>
</tr>
<tr>
<td>
<table class="odpovedi">
<tr>
<td class="licha jednoducha"><input name="7" id="odp7a" type="radio" value="1" /><label for="odp7a">a</label></td>
<td> </td>
<td class="licha jednoducha"><input name="7" id="odp7b" type="radio" value="2" /><label for="odp7b">b</label></td>
</tr>
<tr>
<td> </td>
<td class="licha jednoducha"><input name="7" id="odp7c" type="radio" value="3" /><label for="odp7c">c</label></td>
<td> </td>
</tr>
<tr>
<td class="licha jednoducha"><input name="7" id="odp7d" type="radio" value="4" /><label for="odp7d">d</label></td>
<td> </td>
<td class="licha jednoducha"><input name="7" id="odp7e" type="radio" value="5" /><label for="odp7e">e</label></td>
</tr>
</table>
1 bod
</td>
<td>
<table class="otazky">
<tr><td>7. Goniometrický tvar komplexního čísla ${z=3\i\bigl[\cos(\frac14\pi)+\i\sin(\frac14\pi)\bigr]^3}$ je</td></tr>
<tr><td><label for="odp7a">a) $\sqrt3[\cos(\frac34\pi)+\i\sin(\frac34\pi)]$</label></td></tr>
<tr><td><label for="odp7b">b) $3[\cos(\frac74\pi)+\i\sin(\frac74\pi)]$</label></td></tr>
<tr><td><label for="odp7c">c) $3[\cos(\frac54\pi)-\i\sin(\frac54\pi)]$</label></td></tr>
<tr><td><label for="odp7d">d) $\sqrt{3}[\cos(\frac34\pi)-\i\sin(\frac34\pi)]$</label></td></tr>
<tr><td><label for="odp7e">e) $3[\cos(\frac54\pi)+\i\sin(\frac54\pi)]$</label></td></tr>
</table>
</td>
</tr>
<tr>
<td>
<table class="odpovedi">
<tr>
<td class="licha jednoducha"><input name="8" id="odp8a" type="radio" value="1" /><label for="odp8a">a</label></td>
<td> </td>
<td class="licha jednoducha"><input name="8" id="odp8b" type="radio" value="2" /><label for="odp8b">b</label></td>
</tr>
<tr>
<td> </td>
<td class="licha jednoducha"><input name="8" id="odp8c" type="radio" value="3" /><label for="odp8c">c</label></td>
<td> </td>
</tr>
<tr>
<td class="licha jednoducha"><input name="8" id="odp8d" type="radio" value="4" /><label for="odp8d">d</label></td>
<td> </td>
<td class="licha jednoducha"><input name="8" id="odp8e" type="radio" value="5" /><label for="odp8e">e</label></td>
</tr>
</table>
1 bod
</td>
<td>
<table class="otazky">
<tr><td>8. Výraz ${\left(\dfrac{m}{n}-\dfrac{n}{m}\right) :\dfrac{m^2-n^2}{2m^2n^2}}$ je roven</td></tr>
<tr><td><label for="odp8a">a) ${2m}$, pokud ${m\ne0\lland m\ne n\lland m\ne-n}$</label></td></tr>
<tr><td><label for="odp8b">b) ${2}$, pokud ${m\ne0\lland n\ne0}$</label></td></tr>
<tr><td><label for="odp8c">c) ${2m-n}$, pokud ${m\ne0\lland n\ne0\lland m\ne n\lland m\ne-n}$</label></td></tr>
<tr><td><label for="odp8d">d) ${mn}$, pokud ${n\ne0\lland m\ne n\lland m\ne-n}$</label></td></tr>
<tr><td><label for="odp8e">e) ${2mn}$, pokud ${m\ne0\lland n\ne0\lland m\ne n\lland m\ne-n}$</label></td></tr>
</table>
</td>
</tr>
<tr>
<td>
<table class="odpovedi">
<tr>
<td class="licha jednoducha"><input name="9" id="odp9a" type="radio" value="1" /><label for="odp9a">a</label></td>
<td> </td>
<td class="licha jednoducha"><input name="9" id="odp9b" type="radio" value="2" /><label for="odp9b">b</label></td>
</tr>
<tr>
<td> </td>
<td class="licha jednoducha"><input name="9" id="odp9c" type="radio" value="3" /><label for="odp9c">c</label></td>
<td> </td>
</tr>
<tr>
<td class="licha jednoducha"><input name="9" id="odp9d" type="radio" value="4" /><label for="odp9d">d</label></td>
<td> </td>
<td class="licha jednoducha"><input name="9" id="odp9e" type="radio" value="5" /><label for="odp9e">e</label></td>
</tr>
</table>
1 bod
</td>
<td>
<table class="otazky">
<tr><td>9. Množinou všech řešení rovnice ${\left|\sin x\right|=2+\sin x}$ je</td></tr>
<tr><td><label for="odp9a">a) $\emptyset$</label></td></tr>
<tr><td><label for="odp9b">b) $\bigcup_{k\in\Z} \{\frac32\pi+k\pi\}$</label></td></tr>
<tr><td><label for="odp9c">c) $\bigcup_{k\in\Z} \{\frac32\pi+2k\pi\}$</label></td></tr>
<tr><td><label for="odp9d">d) $\bigcup_{k\in\Z} \{\frac12\pi+k\pi\}$</label></td></tr>
<tr><td><label for="odp9e">e) $\bigcup_{k\in\Z} \{\frac12\pi+2k\pi\}$</label></td></tr>
</table>
</td>
</tr>
<tr>
<td>
<table class="odpovedi">
<tr>
<td class="licha jednoducha"><input name="10" id="odp10a" type="radio" value="1" /><label for="odp10a">a</label></td>
<td> </td>
<td class="licha jednoducha"><input name="10" id="odp10b" type="radio" value="2" /><label for="odp10b">b</label></td>
</tr>
<tr>
<td> </td>
<td class="licha jednoducha"><input name="10" id="odp10c" type="radio" value="3" /><label for="odp10c">c</label></td>
<td> </td>
</tr>
<tr>
<td class="licha jednoducha"><input name="10" id="odp10d" type="radio" value="4" /><label for="odp10d">d</label></td>
<td> </td>
<td class="licha jednoducha"><input name="10" id="odp10e" type="radio" value="5" /><label for="odp10e">e</label></td>
</tr>
</table>
1 bod
</td>
<td>
<table class="otazky">
<tr><td>10. Jestliže ${\log_4y=3\log_4x-1-\frac{1}{2}\log_4(x+2)}$, pak číslo $y$ je rovno</td></tr>
<tr><td><label for="odp10a">a) $\dfrac{3x}{1+\sqrt{x+2}}$</label></td></tr>
<tr><td><label for="odp10b">b) $\dfrac{6x}{x+2}$</label></td></tr>
<tr><td><label for="odp10c">c) $3x-1-\frac{1}{2}(x+2)$</label></td></tr>
<tr><td><label for="odp10d">d) $\dfrac{x^3}{4\sqrt{x+2}}$</label></td></tr>
<tr><td><label for="odp10e">e) $\dfrac{3x}{2x+4}$</label></td></tr>
</table>
</td>
</tr>
<tr>
<td>
<table class="odpovedi">
<tr>
<td class="licha jednoducha"><input name="11" id="odp11a" type="radio" value="1" /><label for="odp11a">a</label></td>
<td> </td>
<td class="licha jednoducha"><input name="11" id="odp11b" type="radio" value="2" /><label for="odp11b">b</label></td>
</tr>
<tr>
<td> </td>
<td class="licha jednoducha"><input name="11" id="odp11c" type="radio" value="3" /><label for="odp11c">c</label></td>
<td> </td>
</tr>
<tr>
<td class="licha jednoducha"><input name="11" id="odp11d" type="radio" value="4" /><label for="odp11d">d</label></td>
<td> </td>
<td class="licha jednoducha"><input name="11" id="odp11e" type="radio" value="5" /><label for="odp11e">e</label></td>
</tr>
</table>
1 bod
</td>
<td>
<table class="otazky">
<tr><td>11. Graf funkce $y=-x^2-4x-1$</td></tr>
<tr><td><label for="odp11a">a) je parabola s vrcholem $V[-2,3]$ a osou rovnoběžnou s osou $y$</label></td></tr>
<tr><td><label for="odp11b">b) je hyperbola se středem $S[-4,-1]$</label></td></tr>
<tr><td><label for="odp11c">c) je parabola s vrcholem $V[4,1]$ a osou rovnoběžnou s osou $y$</label></td></tr>
<tr><td><label for="odp11d">d) je parabola s vrcholem $V[2,3]$ a osou rovnoběžnou s osou $x$</label></td></tr>
<tr><td><label for="odp11e">e) je hyperbola se středem $S[2,3]$</label></td></tr>
</table>
</td>
</tr>
<tr>
<td>
<table class="odpovedi">
<tr>
<td class="licha jednoducha"><input name="12" id="odp12a" type="radio" value="1" /><label for="odp12a">a</label></td>
<td> </td>
<td class="licha jednoducha"><input name="12" id="odp12b" type="radio" value="2" /><label for="odp12b">b</label></td>
</tr>
<tr>
<td> </td>
<td class="licha jednoducha"><input name="12" id="odp12c" type="radio" value="3" /><label for="odp12c">c</label></td>
<td> </td>
</tr>
<tr>
<td class="licha jednoducha"><input name="12" id="odp12d" type="radio" value="4" /><label for="odp12d">d</label></td>
<td> </td>
<td class="licha jednoducha"><input name="12" id="odp12e" type="radio" value="5" /><label for="odp12e">e</label></td>
</tr>
</table>
1 bod
</td>
<td>
<table class="otazky">
<tr><td>12. Maximální definiční obor funkce ${f(x)=\log(x^2-1)}$ je</td></tr>
<tr><td><label for="odp12a">a) $(1,\infty)$</label></td></tr>
<tr><td><label for="odp12b">b) $\langle 1,\infty)$</label></td></tr>
<tr><td><label for="odp12c">c) $(-\infty,-1\rangle \cup\langle 1,\infty)$</label></td></tr>
<tr><td><label for="odp12d">d) $(-\infty,-1)\cup(1,\infty)$</label></td></tr>
<tr><td><label for="odp12e">e) $\R-\{-1,1\}$</label></td></tr>
</table>
</td>
</tr>
<tr>
<td>
<table class="odpovedi">
<tr>
<td class="licha dvojita"><input name="13" id="odp13a" type="radio" value="1" /><label for="odp13a">a</label></td>
<td> </td>
<td class="licha dvojita"><input name="13" id="odp13b" type="radio" value="2" /><label for="odp13b">b</label></td>
</tr>
<tr>
<td> </td>
<td class="licha dvojita"><input name="13" id="odp13c" type="radio" value="3" /><label for="odp13c">c</label></td>
<td> </td>
</tr>
<tr>
<td class="licha dvojita"><input name="13" id="odp13d" type="radio" value="4" /><label for="odp13d">d</label></td>
<td> </td>
<td class="licha dvojita"><input name="13" id="odp13e" type="radio" value="5" /><label for="odp13e">e</label></td>
</tr>
</table>
2 body
</td>
<td>
<table class="otazky">
<tr><td>13. Množinou všech řešení nerovnice ${4|x|+|2-x|<3}$ s neznámou ${x\in\R}$ je</td></tr>
<tr><td><label for="odp13a">a) $(-\frac15,\,\frac13)$</label></td></tr>
<tr><td><label for="odp13b">b) $\langle 0,\,\frac13\rangle $</label></td></tr>
<tr><td><label for="odp13c">c) $(-\frac15,\,2)$</label></td></tr>
<tr><td><label for="odp13d">d) $(-\frac15,\,0\rangle $</label></td></tr>
<tr><td><label for="odp13e">e) $(-\infty,\,\frac13)$</label></td></tr>
</table>
</td>
</tr>
<tr>
<td>
<table class="odpovedi">
<tr>
<td class="licha dvojita"><input name="14" id="odp14a" type="radio" value="1" /><label for="odp14a">a</label></td>
<td> </td>
<td class="licha dvojita"><input name="14" id="odp14b" type="radio" value="2" /><label for="odp14b">b</label></td>
</tr>
<tr>
<td> </td>
<td class="licha dvojita"><input name="14" id="odp14c" type="radio" value="3" /><label for="odp14c">c</label></td>
<td> </td>
</tr>
<tr>
<td class="licha dvojita"><input name="14" id="odp14d" type="radio" value="4" /><label for="odp14d">d</label></td>
<td> </td>
<td class="licha dvojita"><input name="14" id="odp14e" type="radio" value="5" /><label for="odp14e">e</label></td>
</tr>
</table>
2 body
</td>
<td>
<table class="otazky">
<tr><td>14. Bod $E$ je středem strany $CD$ čtverce $ABCD$ o straně $a$. Bod $F$ je průsečíkem úhlopříčky $BD$ s příčkou $AE$. Délka úsečky $EF$ je</td></tr>
<tr><td><label for="odp14a">a) ${\dfrac{\sqrt5\,a}6\,}$</label></td></tr>
<tr><td><label for="odp14b">b) ${\dfrac{\sqrt5\,a}3\,}$</label></td></tr>
<tr><td><label for="odp14c">c) ${\dfrac{\sqrt5\,a}2\,}$</label></td></tr>
<tr><td><label for="odp14d">d) ${\dfrac a5\,}$</label></td></tr>
<tr><td><label for="odp14e">e) ${\dfrac{\sqrt5\,a}4\,}$</label></td></tr>
</table>
</td>
</tr>
<tr>
<td>
<table class="odpovedi">
<tr>
<td class="licha dvojita"><input name="15" id="odp15a" type="radio" value="1" /><label for="odp15a">a</label></td>
<td> </td>
<td class="licha dvojita"><input name="15" id="odp15b" type="radio" value="2" /><label for="odp15b">b</label></td>
</tr>
<tr>
<td> </td>
<td class="licha dvojita"><input name="15" id="odp15c" type="radio" value="3" /><label for="odp15c">c</label></td>
<td> </td>
</tr>
<tr>
<td class="licha dvojita"><input name="15" id="odp15d" type="radio" value="4" /><label for="odp15d">d</label></td>
<td> </td>
<td class="licha dvojita"><input name="15" id="odp15e" type="radio" value="5" /><label for="odp15e">e</label></td>
</tr>
</table>
2 body
</td>
<td>
<table class="otazky">
<tr><td>15. Rovnice $(a-1)x^2+2(a+1)x+a-2=0$ (s neznámou $x$) nemá reálné kořeny právě tehdy, když</td></tr>
<tr><td><label for="odp15a">a) $a\in\R$</label></td></tr>
<tr><td><label for="odp15b">b) $a\in(-\infty,-1)\cup(-1,\frac{1}{5})$</label></td></tr>
<tr><td><label for="odp15c">c) $a\in(-\infty,\frac{1}{5})$</label></td></tr>
<tr><td><label for="odp15d">d) $a\in\R-\{1,\frac{1}{5}\}$</label></td></tr>
<tr><td><label for="odp15e">e) $a\in(\frac{1}{5},1)\cup(1,\infty)$</label></td></tr>
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