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Sagot :

f(x)=(x-2)²-7=x²-2*2*x+2²-7=x²-4x+4-7=x²-4x-3
PAN59
x²-4x-3

a=1
b=-4
c=-3

delta=b²-4ac = 28

x1 = (-b+racine(delta))/2a
= (4+racine(28))/2 = 2+racine(28)

x2 = (-b-racine(delta))/2a
= (4-racine(28))/2 = 2-racine(28)

F(x) = a(x-x1)(x-x2)

F(x) = (x-2-racine(28)) (x-2+racine(28))

F(x) = (x-2-racine(4*7)) (x-2+racine(4*7))

F(x) = (x-2-racine(4)*racine(7)) (x-2+racine(4)*racine(7))

F(x) = (x-2-2*racine(7)) ((x-2+2*racine(7))

F(x) = (x-2(1+racine(7)))  (x-2(1-racine(7)))

(x-2)²-7 = x²-4x+4-7 = x²-4x-3

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