Réponse :

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Bonjour

f(x) = -4x^2 + 2x + 12

g(x) = (2x + 3)(x + 7)

f(x) = (2x + 3)(x - 4) + (2x + 3)(8 - 3x)

f(x) = 2x^2 - 8x + 3x - 12 + 16x - 6x^2 + 24 - 9x

f(x) = -4x^2 + 2x + 12

Factoriser :

f(x) = (2x + 3)(x - 4 + 8 - 3x)

f(x) = (2x + 3)(-2x + 4)

f(x) = -2(2x + 3)(x - 2)

f(x) = g(x)

-2(2x + 3)(x - 2) = (2x + 3)(x + 7)

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

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

(2x + 3)[2(x - 2) + x + 7] = 0

(2x + 3)(2x - 4 + x + 7) = 0

(2x + 3)(3x + 3) = 0

3(2x + 3)(x + 1) = 0

2x + 3 = 0 ou x + 1 = 0

2x = -3 ou x = -1

x = -3/2 ou x = -1