Question

Find the values of a and b so that the polynomial x^3 + 10x^2 ax + b is exactly divisible by x-1 as well as x-2​

Answer 1

Answer:

x

3

−10x

2

+ax+b=f(x)

if f(x) is divisible by (x−1) and (x−2)

⇒f(1)=0=f(2)

f(1)=1−10+a+b=0⇒a+b=9

f(2)=8−40+2a+b=0⇒2a+b=32

∴a=23 b=−14