Question

Sabendo que P(x) = x³ + (a - 2)x² + (b - 4)x - 3 admite as raízes 1 e - 1, o valor de a - b é:

Answer 1

para x=-1

P(x) = x³ + (a - 2)x² + (b - 4)x - 3

p(1)=(-1)³+(a-2).(-1)²+(b-4).(-1)-3

p(1)=-1+a-2-b+4-3

p(1)=a-b-1-2+4-3

p(1)=a-b-3+1

p(1)=a-b-2

sendo : p(1)= 0

a-b-2=0

______

a-b=2 (resposta)

_____________

espero ter ajudado!

boa noite !

Answer 2

$P(x) = x^3 + (a - 2)x^2 + (b - 4)x - 3\\\\\mathsf{Para\ x = 1,}\\\\0 = 1^3 + (a-2).1^2 + (b-4).1 - 3\\0 = 1 + (a-2) + (b-4) - 3\\0 = 1 + a - 2 + b - 4 - 3\\0 = a + b - 8\\a + b = 8\\\\\\\mathsf{Para\ x = -1},\\\\0 = (-1)^3 + (a-2).(-1)^2 + (b-4).(-1) - 3\\0 = -1 + (a-2) + (-b + 4) - 3\\0 = -1 + a - 2 - b + 4 - 3\\0 = a - b - 2\\\boxed{a - b = 2}$

Abraços!