1) 2X^2 + X - 3 = 0
2) [tex]\Delta = 1 - 4 \times 2 \times -3 = 1 + 24 = 25[/tex]
[tex]\sqrt\Delta = 5[/tex]
X1 = (-1 - 5)/(2 * 2) = -6/4 = -3/2
X2 = (-1 + 5)/4 = 4/4 = 1
3) x^2 = X1 et x^2 = X2
X1 est < 0 donc pas de solution
x^2 = 1
x = 1 ou x = -1
4) 2x^4 + x^2 - 3 = 2(x - 1)(x + 1)(x^2 + ax + b)
= 2(x^2 - 1)(x^2 + ax + b)
= (2x^2 - 2)(x^2 + ax + b)
= 2x^4 + 2ax^3 + 2bx^2 - 2x^2 - 2ax - 2b
= 2x^4 + 2ax^3 + (2b - 2)x^2 - 2ax - 2b
Il te suffit maintenant de regarder chaque terme de chaque côté de l’equation
0 = 2ax^3
donc à = 0
(2b - 2)x^2 = x^2
2b - 2 = 1
2b = 1 + 2
b = 3/2
-3 = -2b
b = 3/2
= 2(x - 1)(x + 1)(x^2 + 3/2)
