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Pikachu972
@Pikachu972
May 2019
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Bonjour,
Factoriser, en un produit de trois polynomes de degré 1, le polunome P(x)=4x^3 - 5x^2 -9x.
Résoudre l'équation P(x)=0
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aymanemaysae
Bonsoir ;
P(x) = 4x^3 - 5x² - 9x = x(4x² - 5x - 9) = x(4x² + 4x - 9x - 9)
= x(4x(x + 1) - 9(x + 1)) = x((x + 1)(4x - 9)) = x(x + 1)(4x - 9) .
P(x) = 0 ==> x(x + 1)(4x - 9) = 0
==> x = 0 ou x + 1 = 0 ou 4x - 9 = 0
==> x = 0 ou x = - 1 ou x = 9/4 .
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Pikachu972
vous allez trop vite je ne comprends pas
Pikachu972
P(x) = 4x^3 - 5x² - 9x = x(4x² - 5x - 9) je suis d'accord mais après je ne sais pas pourquoi vous décomposez le 5x en 4x-9x
MAHAM
Bonsoir
p(x)=4x³-5x²-9x
P(x)=x(4x²-5x-9) avec 4x²-5x-9=4(x+1)(x-9/4)
p(x)=4x(x+1)(x-9/4)
p(x)=0⇔4x(x+1)(x-9/4)=0
⇔4x=0 ou x+1=0 ou x-9/4=0
⇔x=0 ou x=-1 ou x=9/4
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P(x) = 4x^3 - 5x² - 9x = x(4x² - 5x - 9) = x(4x² + 4x - 9x - 9)
= x(4x(x + 1) - 9(x + 1)) = x((x + 1)(4x - 9)) = x(x + 1)(4x - 9) .
P(x) = 0 ==> x(x + 1)(4x - 9) = 0
==> x = 0 ou x + 1 = 0 ou 4x - 9 = 0
==> x = 0 ou x = - 1 ou x = 9/4 .
p(x)=4x³-5x²-9x
P(x)=x(4x²-5x-9) avec 4x²-5x-9=4(x+1)(x-9/4)
p(x)=4x(x+1)(x-9/4)
p(x)=0⇔4x(x+1)(x-9/4)=0
⇔4x=0 ou x+1=0 ou x-9/4=0
⇔x=0 ou x=-1 ou x=9/4