Question

find the value of a and b so that the polynomial x³-4x²+ax+b is exactly divisible by x-2 as well as x+1

Answer 1

Answer:

since x-2=0

x=2

so, x^3-4x^2+ax+b=0

=8-16+2a+b=0

=-8+2a+b=0

therefore b=8-2a

similarly x=-1

so,-1-4-a+b=0

=-5-a+b=0

b=5+a

so,8-2a=5+a

=3a=3

a=1

putting value of a=1 in b=5+a we get,

b=6