Question

If f(x)=x4-2x3+3x2-ax+b is a polynomial such that when it is divided by x-1 and
x+1, the remainders are respectively 5 and19, find the value of a and b?

(Final Ans is a=5,b=8.Steps are required..Become the BRAINLIEST if your steps are right!!)

Answer 1

Hello there,

When f(x) is divided by (x+1) and (x-1) , the remainders are 19 and 5 respectively .

∴ f(-1) = 19 and f(1) = 5

(-1)4 – 2 (-1)3 + 3(-1)2 – a (-1) + b = 19

⇒ 1 +2 + 3 + a + b = 19

∴ a + b = 13 ——- (1)

According to given condition f(1) = 5

f(x) = x4 – 2x3 + 3x2 – ax

⇒ 14 – 2 3 + 3 2 – a (1) b = 5

⇒ 1 – 2 + 3 – a + b = 5

∴ b – a = 3 —— (2)

solving equations (1) and (2)

a = 5 and b = 8

HOPE THIS HELPS