Question

If x square -1 is a factor of ax cube + bx square + d , show that a * c =0​

Answer 1

Answer:

x² - 1 is a factor of ax³ + bx² + c

x² - 1 = (x+1)(x-1)

Therefore even (x+1) and (x-1) are factors

Taking x + 1 = 0

x = -1

a(-1)³ + b(-1)² + c = 0

-a + b + c = 0___________________________(1)

Taking x - 1 = 0

x = 1

a(1)³ + b(1)² + c = 0

a + b + c = 0______________________________(2)

Adding (1) and (2),

2 ( b+c) = 0

b+c = 0_________________________________(3)

(1)-(3)

-a = 0

a = 0

∴ a*c = 0

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