Question

if (x^2-1) is a factor of ax^2+bx^3+cx^2+ax+c

Answer 1

Answer:

0

Step-by-step explanation:

Given information is :

x ^2 – 1 is a factor of

f(x) = ax 4 + bx 3 +cx 2 + dx + e

Now (x 2 – 1) can be written as (x + 1) (x – 1)

⇒ (x – 1) and (x + 1) are factors of f(x)

⇒ f(–1) = 0

⇒ a(–1)4 + b(–1)3 + c(–1)2 + d(–1) + e = 0

⇒ a – b + c – d + e = 0

⇒ a + c + e = b + d ..... (equation (1))

and f (1) = 0

⇒ a(1)4 + b(1)3 + c(1)2 + d(1) + e = 0

⇒ a + b + c + d + e = 0

⇒ b + d + b + d = 0 ( from equation 1 )

⇒ 2 (b + d) = 0

⇒ b + d = 0 ..... (equation 2)

After comparing equations (2) and (3) , will get

a + c + e = b + d = 0(Ans)

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