Question

find 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

f(x)=x^3-10x^2-ax+b
f(1)=1-10-a+b=b-a-9
b-a=9---------(1)
f(2)=8-40-2a+b
b-2a=32--------(2)
from (1) and (2)
a=-23
b=-14

Answer 2

f(x)=x^3-10x^2-ax+b
f(1)=1-10-a+b=b-a-9
b-a=9---------(1)
f(2)=8-40-2a+b
b-2a=32--------(2)
from (1) and (2)
a=-23
b=-14