\documentclass[a4paper]{article}%
\usepackage{amsfonts}
\usepackage[T1]{fontenc}
\usepackage[latin1]{inputenc}
\usepackage[francais]{babel}
\usepackage{amsmath,amssymb}
\usepackage[a4paper]{geometry}
\usepackage{xspace}
\usepackage{fancyhdr}
\usepackage{enumerate}
\usepackage{multicol}
\usepackage{theorem}
\usepackage{graphics}
\usepackage{graphicx}
\usepackage{lastpage}
\usepackage[french]{layout}
\usepackage{boxedminipage}
\usepackage{fancybox}
\usepackage{sectsty}
\usepackage{afterpage}
\usepackage{float}
\usepackage{amsmath}
\usepackage{amssymb}%
\setcounter{MaxMatrixCols}{30}
%TCIDATA{OutputFilter=latex2.dll}
%TCIDATA{Version=4.00.0.2312}
%TCIDATA{CSTFile=40 LaTeX article.cst}
%TCIDATA{LastRevised=Monday, March 08, 2004 19:02:26}
%TCIDATA{<META NAME="GraphicsSave" CONTENT="32">}
\geometry{a4paper,marginpar=2cm,lmargin=0cm,rmargin=2cm,marginparsep=0pt,includemp=true,reversemp=true,headsep=-0.2in}
\setlength{\theorempostskipamount}{2\baselineskip}
\theoremheaderfont{\large\bfseries}
{\theorembodyfont{\large\upshape\mdseries}\theoremstyle{break}
\newtheorem{theorem}{Théorème}
}
\newcounter{Cack}[section]
{\theorembodyfont{\large\upshape}\theoremstyle{break}
\newtheorem{acknowledgement}[Cack]{A savoir}
}
\newcounter{Calg}[section]
{\theorembodyfont{\upshape}\theoremstyle{break}
\newtheorem{algorithm}[Calg]{Méthode}
}
\newcounter{Caxi}[section]
{\theorembodyfont{\itshape}
\newtheorem{axiom}[Caxi]{Axiome}
}
\newcounter{Ccas}[section]
{\theorembodyfont{\upshape}
\newtheorem{case}[Ccas]{Cas}
}
\newcounter{Ccorr}[section]
\renewcommand{\theCcorr}{\Roman{Ccorr}}
{\theorembodyfont{\upshape}\theoremstyle{break}
\newtheorem{claim}[Ccorr]{Correction de l'exercice}
}
\newcounter{Cconc}[theorem]
{\theorembodyfont{\large\mdseries}
\newtheorem{conclusion}[Cconc]{Conclusion}
}
\newcounter{Ccond}[theorem]
{\theorembodyfont{\large\mdseries}
\newtheorem{condition}[Ccond]{Hypothèse}
}
\newcounter{Cconj}[section]
{\theorembodyfont{\upshape}
\newtheorem{conjecture}[Cconj]{Conjecture}
}
\newcounter{Ccor}[section]
{\theorembodyfont{\upshape}
\newtheorem{corollary}[Ccor]{Corollaire}
}
\newcounter{Ccrit}[section]
{\theorembodyfont{\upshape}
\newtheorem{criterion}[Ccrit]{Critère}
}
\newcounter{Cdef}[section]
\newcounter{Cnot}[section]
{\theorembodyfont{\large\upshape}\theoremstyle{break}
\newtheorem{definition}[Cdef]{Définition}
\newtheorem{notation}[Cnot]{Notation}
}
\newcounter{Cexa}[section]
{\theorembodyfont{\slshape}
\newtheorem{example}[Cexa]{Exemple}
}
\newcounter{Cexe}[section]
\renewcommand{\theCexe}{\Roman{Cexe}}
{\theorembodyfont{\upshape}\theoremstyle{break}
\newtheorem{exercise}[Cexe]{Exercice}
}
\newcounter{Clem}[section]
{\theorembodyfont{\upshape}
\newtheorem{lemma}[Clem]{Lemme}
}
\newcounter{Cprob}[section]
\renewcommand{\theCprob}{\Roman{Cprob}.}
{\theorembodyfont{\upshape}\theoremstyle{break}
\newtheorem{problem}[Cprob]{Problème}
}
{\theorembodyfont{\large\mdseries}\newcounter{Cprop}[section]\theoremstyle{break}
\newtheorem{proposition}[Cprop]{Propriété}
}
\newcounter{Crem}[section]
{\theorembodyfont{\itshape}
\newtheorem{remark}[Crem]{Remarque}
}
\newcounter{Csol}[section]
{\theorembodyfont{\upshape}\theoremstyle{break}
\newtheorem{solution}[Csol]{Solution}
}
\newcounter{Csum}[section]{\theorembodyfont{\upshape}
\newtheorem{summary}[Csum]{En résumé}
}
\newenvironment{proof}[1][Démonstration]{\noindent\textbf{#1:}}{\ \fbox{cqfd.}}
\renewcommand{\theenumi}{\arabic{enumi}}
\renewcommand{\theenumii}{\alph{enumii}}
\renewcommand{\theenumiii}{\roman{enumiii}}
\renewcommand{\labelenumi}{\textbf{\theenumi)}}
\renewcommand{\labelenumii}{\textbf{\theenumii)}}
\renewcommand{\labelenumiii}{\textbf{\theenumiii.}}
\newcommand{\LeTitre}{}
\newcommand{\Titre}[1]{\title{#1}\renewcommand{\LeTitre}{#1}}
\newcommand{\LaClasse}{}
\newcommand{\Classe}[1]{\renewcommand{\LaClasse} {#1}}
\newcommand{\LaDate}{}
\newcommand{\Date}[1]{\author{#1}\renewcommand{\LaDate} {#1}}
\newcommand{\Duree}[1]{\date{#1}}
\newcommand{\Letablissement}{}
\newcommand{\Etablissement}[1]{\renewcommand{\Letablissement} {#1}}
\newcommand{\Ladiscipline}{}
\newcommand{\Discipline}[1]{\renewcommand{\Ladiscipline}{#1}}
\renewcommand{\thesection}{\Alph{section}}
\renewcommand{\thesubsection}{\thesection\arabic{subsection}}
\renewcommand{\thesubsubsection}{\thesubsection.\arabic{subsubsection}}
\newcounter{exo}
\newcommand{\exo}[1][-]{\stepcounter{exo}\par\vspace{2ex}\noindent{\bf Exercice \theexo\space}\points{#1}\\[1ex]\noindent}
\newcommand{\GN}{\ensuremath{\mathbb{N}}\xspace}
\newcommand{\GR}{\ensuremath{\mathbb{R}}\xspace}
\newcommand{\GC}{\ensuremath{\mathbb{C}}\xspace}
\newcommand{\GZ}{\ensuremath{\mathbb{Z}}\xspace}
\newcommand{\GQ}{\ensuremath{\mathbb{Q}}\xspace}
\newcommand{\GD}{\ensuremath{\mathbb{D}}\xspace}
\newcommand{\ssi}{\ensuremath{\Longleftrightarrow}}
\newcommand{\vecteur}[1]{\overrightarrow{#1\;}}
\newcommand{\oij}{(O;\vecteur{\imath},\vecteur{\jmath})}
\newcommand{\oijk}{\left(O;\vecteur{i},\vecteur{j},\vecteur{k}\right)}
\newcommand{\ouv}{\left(O;\vecteur{u},\vecteur{v}\right)}
\newcommand{\congru}[3]{#1\equiv#2\quad\text{modulo }#3}
\newcommand{\segN}[2]{\left\{ #1\ldots #2\right\}}
\newcommand{\anglevec}[2]{\left(\vecteur{#1};\vecteur{#2}\right)}
\newcommand{\PGCD}{\mathit{PGCD}}
\newcommand{\aire}[1]{$\mathcal{A}ire(#1)$}
\newcommand{\Mod}{\quad\mathit{Mod}}
\newcommand{\Intoo}[2]{\left]#1;#2\right[}
\newcommand{\Intfo}[2]{\left[#1;#2\right[}
\newcommand{\Intof}[2]{\left]#1;#2\right]}
\newcommand{\Intff}[2]{\left[#1;#2\right]}
\newcommand{\Lim}[1]{\underset{#1}{\lim }}
\newenvironment{listerd}
{   \renewcommand{\labelitemi}{\ensuremath{\bulet}}
\renewcommand{\labelitemii}{.}
\begin{itemize}
}{\end{itemize}}
\newcommand{\cro}{
\parbox{1.4cm}{
\setlength{\unitlength}{0.1cm}
\begin{picture}(14,7)
\put(0,0){\vector(2,1){14}}
\end{picture}
}
}
\newcommand{\dec}{
\parbox{1.4cm}{
\setlength{\unitlength}{0.1cm}
\begin{picture}(14,7)
\put(0,7){\vector(2,-1){14}}
\end{picture}
}
}
\everymath{\displaystyle}
\def \points#1%
{\if -#1 \xspace \else {\small ( #1 points )}\xspace\fi }
\DeclareMathOperator{\e}{e}
\begin{document}

%%%%%%%%%%b{gedeonInfo}%%%%%%%%%
%%--Document N° 12955497168563--
%%--Equations du 2° degré liées à une configuration plane--
%%%%%%%%%%e{gedeonInfo}%%%%%%%%%


Copyright (c) 2004, Philippe Ivaldi. Le contenu de ce document peut \^{e}tre
redistribu\'{e} sous les conditions \'{e}nonc\'{e}es dans la Licence pour
Documents Libres version 1.1 ou utl\'{e}rieure.\newline

\begin{exercise}%
%TCIMACRO{\TeXButton{BeginMulticols}{\setlength{\columnseprule}{.4pt}
%\begin{multicols}{2}}}%
%BeginExpansion
\setlength{\columnseprule}{.4pt}
\begin{multicols}{2}%
%EndExpansion%
%TCIMACRO{\TeXButton{TeX field}{\subsection*{Partie A}}}%
%BeginExpansion
\subsection*{Partie A}%
%EndExpansion


On consid\`{e}re l'expression:
\[
A(x)=(6-x)^{2}-(6-x)(6-2x)
\]


\begin{enumerate}
\item D\'{e}velopper, r\'{e}duire et ordonner $A(x)$.

\item Factoriser $A(x)$

\item \label{a3_ieziz}Factoriser l'expression $B(x)=9-A(x)$.

\item R\'{e}soudre alg\'{e}briquement l'\'{e}quation $A(x)=0$.

\item R\'{e}soudre, \`{a} l'aide d'un tableau de signes, l'in\'{e}quation
$A(x)\geqslant0$.
\end{enumerate}

%

%TCIMACRO{\TeXButton{TeX field}{\subsection*{Partie B}}}%
%BeginExpansion
\subsection*{Partie B}%
%EndExpansion
On consid\`{e}re l'expression:
\[
C(x)=(x-6)^{2}-4
\]


\begin{enumerate}
\item D\'{e}velopper, ordonner et r\'{e}duire $C(x)$.

\item Factoriser $C(x)$ .

\item En utilisant les r\'{e}sultats pr\'{e}c\'{e}dents, r\'{e}soudre
l'\'{e}quation:
\[
x^{2}-12x+32=0
\]

\end{enumerate}%

%TCIMACRO{\TeXButton{TeX field}{\subsection*{Partie C}}}%
%BeginExpansion
\subsection*{Partie C}%
%EndExpansion
On consid\`{e}re le trap\`{e}ze rectangle $ABCD$ (voir figure \ref{2805001551}
page \pageref{2805001551}.
\[
AB=6\qquad DC=2\qquad AD=4
\]
On suppose dans la suite de ce probl\`{e}me que $x$ est un nombre r\'{e}el
appartenant \`{a} l'intervalle $[0;4]$.

On pose $AM=x$.

\begin{enumerate}
\item Montrer que l'aire du rectangle $APNM$ est \'{e}gale \`{a}:
\[
f(x)=6x-x^{2}%
\]


\item Repr\'{e}senter la fonction $f$ sur le graphique \ref{28050011616} page
\pageref{28050011616}.

\item En utilisant les r\'{e}sultats de la question \textbf{\ref{a3_ieziz}.}
de la partie A, montrer que $f$ pr\'{e}sente un maximum \'{e}gal \`{a} $9$
pour $x=3$.
\end{enumerate}

%

%TCIMACRO{\TeXButton{TeX field}{\subsection*{Partie D}}}%
%BeginExpansion
\subsection*{Partie D}%
%EndExpansion
Sur le graphique \ref{28050011616} page \pageref{28050011616}, deux courbes
$\Gamma_{1}$ et $\Gamma_{2}$ repr\'{e}sentent l'aire du triangle $BNP$ et
l'aire du trap\`{e}ze $DMNC$ en fonction de $x$.

\begin{enumerate}
\item Identifier ces deux courbes.

\item R\'{e}pondre graphiquement aux questions suivantes:

\begin{enumerate}
\item Pour quelle valeur de $x$, l'aire du triangle $BNP$ est-elle
sup\'{e}rieure \`{a} 5 ?

\item Pour quelle valeur de $x$ l'aire du triangle $BNP$ est elle \'{e}gale
\`{a} l'aire du trap\`{e}ze $DMNC$ ?
\end{enumerate}
\end{enumerate}

%

%TCIMACRO{\TeXButton{EndMulticols}{\end{multicols}}}%
%BeginExpansion
\end{multicols}%
%EndExpansion
%

%TCIMACRO{\FRAME{fpFU}{2.9033in}{2.0888in}{0pt}{\Qcb{$\quad$}}{\Qlb{2805001551}%
%}{fig.eps}{\special{ language "Scientific Word";  type "GRAPHIC";
%maintain-aspect-ratio TRUE;  display "USEDEF";  valid_file "F";
%width 2.9033in;  height 2.0888in;  depth 0pt;  original-width 2.7447in;
%original-height 1.9684in;  cropleft "0";  croptop "1";  cropright "1";
%cropbottom "0";  filename 'Include/fig.eps';file-properties "XNPEU";}}}%
%BeginExpansion
\begin{figure}
[p]
\begin{center}
\includegraphics[
height=2.0888in,
width=2.9033in
]%
{Include/fig.eps}%
\caption{$\quad$}%
\label{2805001551}%
\end{center}
\end{figure}
%EndExpansion%
%TCIMACRO{\FRAME{fpFU}{2.4541in}{5.2885in}{0pt}{\Qcb{$\quad$}}%
%{\Qlb{28050011616}}{graph.eps}{\special{ language "Scientific Word";
%type "GRAPHIC";  maintain-aspect-ratio TRUE;  display "USEDEF";
%valid_file "F";  width 2.4541in;  height 5.2885in;  depth 0pt;
%original-width 3.9153in;  original-height 8.4881in;  cropleft "0";
%croptop "1";  cropright "1";  cropbottom "0";
%filename 'Include/graph.eps';file-properties "XNPEU";}}}%
%BeginExpansion
\begin{figure}
[pp]
\begin{center}
\includegraphics[
height=5.2885in,
width=2.4541in
]%
{Include/graph.eps}%
\caption{$\quad$}%
\label{28050011616}%
\end{center}
\end{figure}
%EndExpansion


%\newrgbcolor{gris}{.7 .7 .7}
%\begin{figure}[p]
%\begin{center}
%\begin{pspicture}(-0.5,-0.5)(8.5,20)
%\psgrid[gridlabels=0,subgriddiv=10,subgridwidth=0.2pt,
%subgriddots=0,gridwidth=0.1pt,griddots=0,subgridcolor=gris,xunit=2,yunit=2]%
%(0,0)(0,0)(4,10)
%\psaxes[linewidth=0.6pt,xunit=2,yunit=2]{->}(0,0)(-0.5,-0.5)(4.5,10.5)
%\uput{.2}[225](0,0){$0$}
%\psplot[plotpoints=100,xunit=2,yunit=2,linewidth=1pt]{0}{4}{x 2 exp 2 div}
%\psplot[plotpoints=100,xunit=2,yunit=2,linewidth=1pt]{0}{4}%
%{x -4 add 2 exp 2 div}
%\end{pspicture}
%\end{center}
%\caption{{}$\quad$}%
%\label{28050011615}%
%\end{figure}

\end{exercise}


\end{document}