Bonsoir,
2x^2 + 5x + 3 = 0
As tu vu le discriminant ? Bonne question !
Si oui :
Delta = (5)^2 - 4 * 2 * 3
Delta = 25 - 24
Delta = 1
Vdelta = 1 > 0 donc 2 solutions possibles
X1 = (-5 - 1)/(2 * 2) = -6/4 = -3/2
X2 = (-5 + 1)/(2 * 2) = -4/4 = -1
Si tu ne connais pas alors :
Il faut remplacer x = X + a
2(X + a)^2 + 5(X + a) + 3 = 0
2(X^2 + 2aX + a^2) + 5X + 5a + 3 = 0
2X^2 + 4aX + 2a^2 + 5X + 5a + 3 = 0
2X^2 + X(4a + 5) + 2a^2 + 5a + 3 = 0
Il faut trouver à pour que 4a + 5 = 0
4a = -5
a = (-5/4)
On remplace a dans l’expression :
2X^2 + X(4 * (-5/4) + 5) + 2 * (-5/4)^2 + 5 * (-5/4) + 3 = 0
2X^2 + X(-5 + 5) + 2 * 25/16 - 25/4 + 3 = 0
2X^2 + 25/8 - 50/8 + 24/8 = 0
2X^2 = 1/8
X^2 = 1/16
X = 1/4
Ou X = -1/4
On remplace X dans l’expression de x, il y aura deux solutions :
x1 = 1/4 - 5/4
x1 = -4/4
x1 = -1
x2 = -1/4 - 5/4
x2 = -6/4
x2 = -3/2
Factoriser :
64 - 36x^2 = 8^2 - (6x)^2 = (8 - 6x)(8 + 6x) =
2(4 - 3x) * 2(4 + 3x) = 4(4 - 3x)(4 + 3x)
