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Terminale STI2D

Fiche de cours de mathématique: trinôme du second degré
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Description
Fiche de cours de mathématique: trinôme du second degré
Niveau
Terminale STI2D
Mots clé
fiche de cours, second degré, 2nd degré, trinôme
Voir aussi:

Documentation sur LaTeX lien vers la documentation Latex
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Source Latex 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\newcommand{\TITLE}{Trinôme du second degré}
\author{Y. Morel}
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Pour un trinôme du second degré: 
\ul{$f(x)=ax^2+bx+c$}, où $a$, $b$ et $c$ sont trois réels, et $a\not=0$. 

%\vspq
Le discriminant du trinôme est \fbox{$\Delta=b^2-4ac$}.
\enmp

\medskip
\hspace{-.5cm}
\begin{tabular}{|p{1.5cm}|p{3.6cm}|p{3.4cm}|p{3.4cm}|} \cline{2-4}
  \multicolumn{1}{c|}{}& 
  \raisebox{-0.2cm}[0.3cm][0.5cm]{\ct{$\Delta>0$}} & 
  \raisebox{-0.2cm}[0.3cm][0.5cm]{\ct{$\Delta=0$}} & 
  \raisebox{-0.2cm}[0.3cm][0.5cm]{\ct{$\Delta<0$}} \\\hline

  \vspace{0.cm}
  \small Solution(s) de \[f(x)=0\]

  \vspace{-0.4cm}

  &\small 2 solutions réelles 

  distinctes: 

  \[ x_1=\frac{-b-\sqrt{\Delta}}{2a}\]
  \[ x_2=\frac{-b+\sqrt{\Delta}}{2a}\] 
  &\small une solution réelle unique (double) : 

  \[x_0=\frac{-b}{2a}\]

  & \vspace{0.5cm}\small pas de solution réelle \\\hline

  \vspace{0.1cm}
  Tableau \mbox{de signe}
  \vspace{.4cm}
  &
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  \vspace{1em}
  Courbe \[a>0\]

  \vspace{.2cm}\ \, 
  &

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  \\\hline

  \vspace{1em}
  Courbe 
  \[a<0\]

  \vspace{.2cm}\ \, 
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  \\\hline

\end{tabular}

\enmp

\end{document}

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