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14021208
@14021208
April 2019
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Bonjours j'ai besoin d'aide pour un dm de mathématiques :
Soit la fonction définie sur R par :
f(X)=(2x+1)(x-3)+(2x+1)(3x+2)
1- développer
2-factoriser
en utilisant l’expression la plus adaptée de f(x):
calculer f(0) f(-1/2) f(racine de 2)
résoudre f(x) = 0 et f(x)= 8x au carrée
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Bonjour
1) Développer
f(x) = (2x+1)(x-3)+(2x+1)(3x+2)
f(x) = 2x²-6x+x-3+6x²+4x+3x+2
f(x) = 8x²+2x-1
2) Factoriser
f(x) = (2x+1)(x-3+3x+2)
f(x) = (2x+1)(4x-1)
3)
f(0) = 8(0)²+2(0)-1 = -1
f(-1/2)= (2(-1/2)+1)(4(-1/2)-1) = 0 ( -3) = 0
f(V2) = 8(V2)² + 2(V2) -1 = 16 + 2V2 - 1 = 15 + 2V2
4)
f(x) = 0
f(x) =(2x+1)(4x-1) = 0 produit de facteurs nul si un des facteur est nul
soit 2x+1 = 0 pour x = -1/2 ou 4x-1 = 0 pour x = 1/4
5)
f(x) = 8x²
8x²+2x-1 = 8x² revient à 2x-1 = 0 pour x = 1/2
2 votes
Thanks 1
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Verified answer
Bonjour1) Développer
f(x) = (2x+1)(x-3)+(2x+1)(3x+2)
f(x) = 2x²-6x+x-3+6x²+4x+3x+2
f(x) = 8x²+2x-1
2) Factoriser
f(x) = (2x+1)(x-3+3x+2)
f(x) = (2x+1)(4x-1)
3)
f(0) = 8(0)²+2(0)-1 = -1
f(-1/2)= (2(-1/2)+1)(4(-1/2)-1) = 0 ( -3) = 0
f(V2) = 8(V2)² + 2(V2) -1 = 16 + 2V2 - 1 = 15 + 2V2
4)
f(x) = 0
f(x) =(2x+1)(4x-1) = 0 produit de facteurs nul si un des facteur est nul
soit 2x+1 = 0 pour x = -1/2 ou 4x-1 = 0 pour x = 1/4
5)
f(x) = 8x²
8x²+2x-1 = 8x² revient à 2x-1 = 0 pour x = 1/2