bonjour, quelqu'un peut m'aider pour cet exercice merci: 1)P(x)=2x au carré-7x+3 2)P(x)=-7 au carré+4x+11 3)P(x)=x au carré+5/2x+1 a) résoudre les equations P(x

P(x) = 2x^2 - 7x + 3 = 0

On calcule le discriminant :P(x) = 2x^2 - 7x + 3 = 0

On calcule le discriminant :

Delta = (-7)^2 - 4 * 2 * 3
Delta = 49 - 24
Delta = 25
V(delta) = 5 > 0 donc 2 solutions

X1 = (-7 - 5)/(2*2) = (-12)/4 = (-3)
X2 = (-7 + 5)/4 = (-2)/4 = (-1/2)

P(x) = (x - 3)(x - 1/2)

Établir le tableau de signe :

X. |. -inf. 1/2. 3. +inf |
---------------------------------------
X-3. |. - |. - O. +
X-1/2 |. - O. +. |. +
--------------------------------------
p(x). |. +. O. - O. +

2) p(x) = -7x^2 + 4x + 11

Delta = 4^2 - 4*(-7)*11
Delta = 16 + 308
Delta = 324
V(delta) = 18 > 0 donc 2 solutions

X1 = (4 - 18)/(2*-7)= (-14)/(-14) = 1
X2 = (4+18)/(-14) = 22/(-14) = (-11/7)

P(x) = (x+1)(x-11/7)


Signe :

X. | -inf. -1. 11/7. +inf. |
------——-——————————————
X+1. |. - O. +. |. +
X-11/7 |. - |. - O. +.
-----------------------------------------
P(x) |. +. O. - O. +


3) p(x) = x^2 +5/2x +1

Delta = (5/2)^2 -4*1*1
Delta = 25/4 -4
Delta = 25/4 - 16/4
Delta = 9/4
V(delta) = 3/2

X1 = (5/2 - 3/2)/2 = (2/2)/2 = 1/2
X2 = (5/2 + 3/2)/2 = (8/2)/2 = 4/2 = 2

P(x) = (x + 1/2)(x + 2)

Tableau :

X. |. -inf. -2. -1/2. +inf |
----------------------------------------
X+1/2 |. - |. - O. +
X+2. |. - O. +. |. +
-----------------------------------------
P(x) |. +. O. - O. +