mathpolynome.py

Created on February 07, 2021

591 Bytes

(a+b)2= a2+2ab+b2
(a-b)2= a2-2ab+b2
(a+b)(a-b)= a2-b2

f(x)= ax2+bx+c (developee)
f(x)= a(x-A)2+B (canonique)
    = a(x-x0)2
f(x)= a(x-x1)(x-x2) (factorisee)
a[(x+b/2a)2-D/4a2] (dev to canon)

D= b2-4(a)(c)
x0= [-b/2a]
x1= [-b-sqrt(D)]/2a
x2= [-b+sqrt(D)]/2a
si D = 0 -> 1 racine double (x0)
si D < 0 -> pas de racine/solution
si D > 0 -> 2 racines (x1 et x2)

coord sommet parabole = (-b/2a ; -D/4a)

Tout polynome f a pour ensemble de
definition Df = ]-inf ; +inf[
Un trinome est du signe de a sauf
entre ses racines si elles existent

[x2-Sx+P]= 0
S= [-b/a]
P= [c/a]

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