Question

10. Let R1and R2are the remainders when the polynomials
x^3+ 2x^2– 5ax – 7 and x^3+ax^2 – 12x + 6 are divided by (x + 1) and
(x - 2) respectively. If 2R1+R2 = 6, find the value of a.

Answer 1

By remainder theorm
For 1st polynomial
P(-1) =R1
R1=5a-6

For 2nd polynomial
P(2)= R2
R2=4a-10

For R1 and R2
A=2