Question

if x+a is a factor of the polynomial x2+px+q and x2+mx+n prove that a=n-q/m-p

Answer 1

here is your solution
see picture

Answer 2

x²+px+q=0,
=>a²-ap+q=0 [since x+a is a factor]
again,
x²+mx+n=0
=>a²-ma+n=0

now, a²-ap+q=a²-ma+n
=>am-ap=n-q
=>a=(n-q)/(m-p)