Question

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

Answer 1

$x^3+10x^2+ax+b$

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