If x+a is a factor of x^2+px+q and x^2+px +q then prove that a=n-q/m-p

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Solution

p(x)= x2+px+q

g(x)= x+a

x = -a

p(-a)= a2-ap+q=0 1st equatioon

p1(x)=x2+mx+n

p1(-a)=a2-am+n=0 2nd equation

on equating 1 and 2

a2-am+n=a2-ap+q

-am+ap=q-n

-a(m-p)=q-n

-a= q-n/m-p

a= n-q/m-p

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