Question

if x-a is factor of 3x^2-mx-nx,then prove that a=m+n/3

Answer 1

According to the remainder theorem,

p(a)=3a^2-ma-na

Since x-a is a factor of the polynomial

therefore 3a^2-ma-na=0.

a(3a-m-n)=0

3a-m-n=0

3a=m+n

Therefore, a=m+n/3

Verified.