\title{Factorisation des polynômes de degré 2}


\author{Damien Delwarde}

\precision{10000000000}
\format{html}
\computeanswer{no}



\integer{lambda=random(-5,-4,-3,-2,-1,1,2,3,4,5)}
\integer{alpha=random(-5..5)}
\integer{beta=random(-5..5)}
\text{polynome1=\lambda*(x-\alpha)*(x-\beta)}

\integer{a=random(-5,-4,-3,-2,-1,1,2,3,4,5)}
\integer{b=random(-5..5)}
\integer{c=random(-5..5)}
\integer{Delta=(\b)^2-4*\a*\c}
\if{\Delta>=0}{\integer{a=random(2..5)},\integer{b=rand

om(-2..2)},\integer{c=random(1..5)} }
\text{polynome2=\a*x^2+\b*x+\c}
\text{polyn2=\a*(x^2+(\b/\a)*x+(\c/\a))}
\text{pol2=maxima(\polyn2)}
\text{polyn1=maxima(expand(\polynome1))}
\text{p1=maxima(\polyn1)}
\text{p2=maxima(\polynome2)}

\text{factorise=maxima(\lambda*(x-(\alpha))*(x-(\beta))

)}

\text{p=randitem(\p1,\p2)}


\text{rlist=r1,r2}




\if{\p issametext 

\p1}{\text{n=1}}{\text{n=2}}

		
\text{rep=item([\n..\n],\rlist)}

\steps{\rep}

\statement{ 

polyn1=\(\polynome1)<p>
p1=\(\p1)<p>
polyn2=\(\polynome2)<p>
p2=\(\p2)<p>
p=\(\p)<p>



Factorisez le polynôme p sous la forme \( 

lambda(x-alpha)(x-beta) )<p>
<center> On a, pour tout 

\(x) réel : \( p(x) )= \embed{\rep,35} </center> 
	

	}

			


\answer{}{\factorise}{type=algexp}
\answer{}{\p2,\pol2}{type=algexp}