Question

Let L₁ and L₂ be the remainders when the polynomials x³+2x²-5ax-7 and x³+ax²-12x+6 are divided by (x+1) and (x-2) respectively. If 2L₁+L₂=6 then the value of a= *

Answer 1

Answer Key

By remainder theorem $L_{1}=(-1)^3+2(-1)^2-5a(-1)-7=-1+2+5a-7=5a-6$, and $L_{2}=(2)^3+a(2)^2-12(2)+6=8+4a-24+6=4a-10$.

Given equation $2L_{1}+L_{2}=6$.

Solution

Given equation

$\implies 2L_{1}+L_{2}=10a-12+4a-10=14a-22$

$\implies 14a-22=6$

$\implies 14a=28$

$\implies \boxed{a=2}$