Soit f(x) = [tex]3/4x^{3} - 6x^{2} + 10x : a) Factoriser f(x)[/tex]

Bonsoir

Factorisons f(x)

(3/4)x^3 - 6x² + 10x  simplifions l'expression en factorisant par x
x ((3/4)x² - 6x + 10 = 0
 x = 0     ou ((3/4)x² - 6x + 10 = 0

((3/4)x² - 6x + 10 = 0
Calculons Δ
Δ = b² - 4ac pour a = 3/4, b = -6 et c = 10
Δ = (-6)² - 4(3/4)(10) = 36 - 30 = 6
√Δ = √6

x1 =( -b - √Δ) / 2a
x1 = (6 - √6) / (3/2)
x1 = (12 - 2√6) / 3 

x2 = ( -b + √Δ) / 2a
x2 = (6 + √6) / 3/2
x2 = (12 + 2√6) / 3 


S = {0;(12 - 2√6) / 3;(12 + 2√6) / 3  }


x(x - 12 +√6)/3)(x-12-√6)/3