Question

please let me know what will be the answer to the following question no.10

Answer 1

(2x+1) is a factor of equation
2x^2-5x+p -------------- |eq.1|
and 2x^2+5x+q---------|eq.2|
i.e. x=(2x+1)
so putting value of x in eq. 1 and 2
eq.1:
p(x)=2x^2-5x+p
p(2x+1)=2(2x+1)^2-5(2x+1)+p
0=2(4x^2+1+2x)-5(2x+1)+p
0=(8x^2+2+4x)-(10x+5)+p
0=8x^2+2+4x-10x-5+p
0=8x^2+4x-10x+2+p
0=8x^2-6x+2+p
p=(-8)x^2+6x-2
-p=8x^2-6x-2
-p=8x^2-(8x-2x)-2
-p=8x^2-8x+2x-2
-p=8x(x-1)+2(x-1)
-p=(8x+2)(x-1)
-p=-2÷8 , 1