Question

the polynomial ax^3+3x^2-3 and 2x^3-5x+a when divided by x-4 leaves the remainders p and q respectively . Find the value of a if 2p=q

Answer 1

let f(x)=ax^3+3x^2-3
g(x)=2x^3-5x+a
given f(4)=p
g(4)=q

a(4)^3+3(4)^2-3=p
64a+48=p
64a-p=-48----------(1)

2(4)^3-5x+a=2p. (2p=q)
128-20+a=2p
a-2p=-108-----------(2)
from eq. 1 we get,

p=48+64a
substitute the value in equation 1
a-2(48+64a)=-108
a-96+128a=-108
129a-96=-108
129a=-12
a=-12/129