Bonsoir,
1) Forme 1 : f(x) = 4(x-5)²-9 = 4(x²-10x+25)-9 = 4x²-40x+100-9 = 4x²-40x+91
Forme 2 : f(x) = (2x-13)(2x-7) =4x²-14x-26x+91 = 4x²-40x+91
2) La forme factorisée de f est la forme 2.
3)a. f(x) = 0
On utilise la forme factorisée pour avoir une équation produit nul (a×b = 0)
On a alors :
(2x-13)(2x-7) = 0
Soit 2x-13 = 0 donc 2x = 13 <=> x = 13/2
Soit 2x-7 = 0 donc 2x = 7 <=> x = 7/2
b. f(0) = 4×0²-40×0+91 = 91
c. f(x) = -9
4(x-5)²-9 = -9
4(x-5)² = 0 <=> x-5 = 0 <=> x = 5
d. f(√2) = 4×(√2)²-40√2+91 = 4×2-40√2+91 = 8-40√2+91 = 99-40√2
e. f(x) = 91
4x²-40x+91 = 91
4x²-40x = 0
4x(x-10) = 0
Soit 4x = 0 <=> x = 0
Soit x-10 = 0 <=> x = 10
