Question

If both (x-2) and (x-1/2) are factors of (px²+5x+r) , show that p=r
( with procedure please )

Answer 1

if x=2 is a factor of polynomial then
p(2)^2 +5(2)+r=0
4p+10+r=0------(1)

if x=1/2 is factor of polynomial then
p(1/2)^2 +5(1/2)+r=0
p/4+5/2+r=0
(p+10+4r)/4=0
p+10+4r=0-----(2)
on solving eqn (1) &(2)
we get
r= -2 & p= -2

so r=p