\documentclass[12pt,a4paper,landscape]{article}
\usepackage[utf8]{inputenc}
\usepackage[french]{babel}
\usepackage[T1]{fontenc}
\usepackage[margin=1cm]{geometry}
\usepackage{nopageno}
\usepackage{pas-math}
\usepackage{lmodern}
\usepackage{tkz-tab}
	\usetikzlibrary{calc,shapes.geometric,decorations.pathmorphing}
\author{Stéphane Pasquet}
\begin{document}
\begin{center}
\begin{tikzpicture}[->,>=latex]
\node[rectangle,draw,rounded corners,inner sep=1ex,align=center,text width=5cm] (F) {$P(x)=ax^2+bx+c$};
%
\node at ($(F)+(-10,0)$) {https://courspasquet.fr};
\node at ($(F)+(10,0)$) {https://mathweb.fr};
\node[rectangle,draw,rounded corners,inner sep=1ex,align=center,text width=5cm] (D) at ($(F.south)+(0,-1)$) {$\Delta=b^2-4ac$};
\draw[very thick] (F.south)--(D.north);
\node[rectangle,draw=red,rounded corners,inner sep=1ex,align=center,text width=5cm,fill=red!10,minimum height=3cm] (P) at ($(D.south east)+(+4,-3)$) {Les racines sont :\\[5pt]$x_1=\dfrac{-b-\sqrt\Delta}{2a}$\\[8pt]$x_2=\dfrac{-b+\sqrt\Delta}{2a}$};
\draw[very thick,color=red] (D.360) to[bend left=20] (P.north);
\node[fill=white,text width=2cm,draw=red,fill=red!10,align=center,shape=ellipse,inner xsep=0pt] at ($0.5*(D.360)+0.5*(P.north)+(0.5,0.3)$) {$\Delta>0$};
\node[rectangle,draw=red,rounded corners,inner sep=1ex,align=center,text width=5cm,fill=red!10,minimum height=1.5cm] (f1) at ($(P.south)+(0,-1.5)$) {Factorisation :\\$a(x-x_1)(x-x_2)$};
\draw[very thick,color=red] (P.south)--(f1.north);
\node[below,rectangle,draw=red,rounded corners,inner sep=1ex,align=center,text width=5cm,fill=red!10] (g1) at ($(f1.south)+(0,-1)$) {
\begin{tikzpicture}
\draw[->] (-2,0) -- (2,0);
\draw[->] (0,-2) -- (0,2);
\clip (-2,-2) rectangle (2,2);
\draw[very thick,violet] plot[domain=-2:2,samples=100] (\x,{(\x-1.5)*(\x-0.5)});
\node[violet,text width=2cm,right] at (-2,1.5) {$a>0$};
\draw[very thick,green!50!black] plot[domain=-2:2,samples=100] (\x,{-(\x+1.5)*(\x+0.5)});
\node[green!50!black,text width=2cm] at (1.6,-1.5) {$a<0$};
\fill[green!50!black] (-0.5,0) circle (2pt) node[above] {$x_1$};
\fill[green!50!black] (-1.5,0) circle (2pt) node[above] {$x_2$};
\fill[violet] (0.5,0) circle (2pt) node[below] {$x_1$};
\fill[violet] (1.5,0) circle (2pt) node[below] {$x_2$};
\fill[violet] (1,-0.25) circle (2pt) node[below] {$S$};
\fill[green!50!black] (-1,0.25) circle (2pt) node[above] {$S$};
\end{tikzpicture}
};
\draw[very thick,color=red] (f1.south)--(g1.north);
% ----------------------------------------------------->
\node[rectangle,draw=blue,rounded corners,inner sep=1ex,align=center,text width=5cm,fill=blue!10,minimum height=3cm] (Z) at ($(D.south)+(0,-3)$) {Une racine \og double \fg{}:\\[6pt]$x_S=\dfrac{-b}{2a}$ };
\draw[very thick,color=blue] (D.south) -- (Z.north) node[midway,fill=white,text width=2cm,draw=blue,fill=blue!10,align=center,shape=ellipse,inner xsep=0pt] {$\Delta=0$};
\node[rectangle,draw=blue,rounded corners,inner sep=1ex,align=center,text width=5cm,fill=blue!10,minimum height=1.5cm] (f2) at ($(Z.south)+(0,-1.5)$) {Factorisation :\\$a(x-x_S)^2$};
\draw[very thick,color=blue] (Z.south)--(f2.north);
\node[below,rectangle,draw=blue,rounded corners,inner sep=1ex,align=center,text width=5cm,fill=blue!10] (g2) at ($(f2.south)+(0,-1)$) {
\begin{tikzpicture}
\draw[->] (-2,0) -- (2,0);
\draw[->] (0,-2) -- (0,2);
\clip (-2.5,-2) rectangle (2.5,2);
\draw[very thick,violet] plot[domain=-2:2,samples=100] (\x,{(\x-0.5)*(\x-0.5)});
\node[right,text width=2cm,violet] at (-2.4,1.5) {$a>0$};
%\node[right,text width=2cm,green!50!black] at (-2,-1.75) {$a<0$};
\draw[very thick,green!50!black] plot[domain=-2:1,samples=100] (\x,{-(\x+0.5)*(\x+0.5)}) node[above right,inner ysep=0.75em] {$a<0$};
\fill[green!50!black] (-0.5,0) circle (2pt) node[above] {$x_S$};
\fill[purple] (0.5,0) circle (2pt) node[below] {$x_S$};
\end{tikzpicture}
};
\draw[very thick,color=blue] (f2.south)--(g2.north);
%------------------------------------------------------->
\node[rectangle,draw=brown,rounded corners,inner sep=1ex,align=center,text width=5cm,fill=yellow!20,minimum height=3cm] (N) at ($(D.south west)+(-4,-3)$) {Pas de racine dans \R};
\draw[very thick,color=brown] (D.180) to [bend right=20] (N.north);
\node[fill=white,text width=2cm,draw=brown,fill=yellow!10,align=center,shape=ellipse,inner xsep=0pt] at ($0.5*(D.180)+0.5*(N.north)+(-.5,0.3)$) {$\Delta<0$};
\node[rectangle,draw=brown,rounded corners,inner sep=1ex,align=center,text width=5cm,fill=yellow!20,minimum height=1.5cm] (f3) at ($(N.south)+(0,-1.5)$) {Pas de factorisation};
\draw[very thick,color=brown] (N.south)--(f3.north);
\node[below,rectangle,draw=brown,rounded corners,inner sep=1ex,align=center,text width=5cm,fill=yellow!20] (g3) at ($(f3.south)+(0,-1)$) {
\begin{minipage}{5cm}
\begin{tikzpicture}[>=]
\draw[->] (-2,0) -- (2,0);
\draw[->] (0,-2) -- (0,2);
\clip (-2.5,-2) rectangle (2.5,2);
\draw[very thick,violet] plot[domain=-2:2,samples=100] (\x,{(\x-1.5)*(\x-0.5)+1});
\node[violet,text width=2cm,right] at (-1.5,1.5) {$a>0$};
\draw[very thick,green!50!black] plot[domain=-2:2,samples=100] (\x,{-(\x+1.5)*(\x+0.5)-1});
\node[green!50!black,right,text width=2cm] at (0,-1.5) {$a<0$};
\fill[violet] (1,.75) circle (2pt) node[below] {$S$};
\fill[green!50!black] (-1,-.75) circle (2pt) node[above] {$S$};
\end{tikzpicture} 
\end{minipage}
};
\draw[very thick,color=brown] (f3.south) -- (g3.north);
%------------------------------------------------------->
\begin{scope}[shift={($(g1.south)+(-4.5,-1)$)},>=,draw=red]
\tkzTabInit[lgt=1.3,espcl=2,color,colorC=red!10,colorL=red!10,colorV=red!10]{$x$/0.5,$P(x)$/0.75}{$-\infty$,$x_1$,$x_2$,$+\infty$}
\tkzTabLine{,\text{sgn}(a),z,\text{sgn}(-a),z,\text{sgn}(a)}
\end{scope}
\draw[very thick,color=red] (g1.south) -- ($(g1.south)+(0,-1)$);
%------------------------------------------------------->
\begin{scope}[shift={($(g2.south)+(-3,-3)$)},>=,draw=blue]
\tkzTabInit[lgt=1.3,espcl=2,color,colorC=blue!10,colorV=blue!10,colorL=blue!10]{$x$/0.5,$P(x)$/0.75}{$-\infty$,$x_S$,$+\infty$}
\tkzTabLine{,\text{sgn}(a),z,\text{sgn}(a)}
\end{scope}
\draw[very thick,color=blue] (g2.south) -- ($(g2.south)+(0,-3)$);
%------------------------------------------------------->
\begin{scope}[shift={($(g3.south)+(-2.2,-1)$)},>=,draw=brown]
\tkzTabInit[lgt=1.3,espcl=2,color,colorC=yellow!10,colorV=yellow!10,colorL=yellow!10]{$x$/0.5,$P(x)$/0.75}{$-\infty$,$+\infty$}
\tkzTabLine{,\text{sgn}(a)}
\end{scope}
\draw[very thick,color=brown] (g3.south) -- ($(g3.south)+(0,-1)$);
\node[draw,fill=pink,decorate,decoration={random steps,segment length=2mm}] at ($(g3.south)+(0,-4)$) {sgn($a$) : signe de $a$};
\node[draw,fill=pink,decorate,decoration={random steps,segment length=2mm}] at ($(g1.south)+(0,-4)$) {sgn($-a$) : signe opposé de $a$};
\end{tikzpicture}
\end{center}
\end{document}