Question

if both(x+1)and (x-1) are factors ofax^3+x^2-2x+b. find values of a and b​

Answer 1

Answer:

a = - 1 and b = - 4

Step-by-step explanation:

  As ( x + 1 ), ( x - 1 ) are the roots of this polynomial( say f(x) ),f(x) will be 0 when x = 1 or - 1.

 When x = - 1

⇒ f(x) = 0

⇒ f(-1) = 0

⇒ a(-1)^3 + (-1)^2 - 2(-1) + b = 0

⇒ - a + 1 + 2 + b = 0

⇒ b - a + 3 = 0

⇒ a = b + 3

   When x = 1

⇒ f(1) = 0

⇒ a(1)^3 + (1)^2 - 2(1) + b =0  

⇒ a + 1 - 2 + b = 0

⇒ a + b - 1 = 0

⇒ b + 3 + b - 1 = 0     { a = b + 3 }

⇒ 2a + 2 = 0

⇒ a = - 1

   - 1 = b + 3

    - 4 = b