Subversion Repositories wimsdev

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<p>Trinôme \(f(x)=a*x^2+b*x+c) avec \(a \ne 0),
\(\Delta=b^2-4 a c),
\(f(x) = a (x - x_S)^2 + y_S) avec \(x_S=\frac{-b}{2a}) et \(y_S=f(x_S))</p>
<table class="wimscenter">
<tr><td></td><td>\(\Delta \lt 0)</td>
<td>\(\Delta = 0)</td><td>\(\Delta \gt 0)</td></tr>
<tr><td>\(a \gt 0)</td>
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<br>cas 1<br> \tab1
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<br>cas 2<br>\tab2
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<br>cas 3<br>\tab3
</td></tr>
<tr><td>\(a \lt 0)</td><td>
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}<br>\tab4<br>cas 4
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<br>\tab5<br>cas 5
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<br>\tab6<br>cas 6
</td>
</tr>
<tr><td>Racines<br>Solutions de<br>\(f(x) = 0)</td><td>Pas de racine.</td><td>\(x_S = x_1 = x_2 = \frac{-b}{2 a})</td><td>\(x_1=\frac{-b-\sqrt{\Delta}}{2 a}) et \(x_2=\frac{-b+\sqrt{\Delta}}{2 a})</td></tr>
<tr><td>Factorisation</td><td>Pas de factorisation</td><td>\(f(x) = a (x - x_S)^2)</td><td>\(f(x) = a (x - x_1) (x - x_2))</td></tr>
</table>