SOLUTION: If x+a is a factor of the polynomial x^2 + px + q and x^2 + mx + n, then prove that a = (n-q) / (m-p).

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: If x+a is a factor of the polynomial x^2 + px + q and x^2 + mx + n, then prove that a = (n-q) / (m-p).      Log On


   

Question 756502: If x+a is a factor of the polynomial x^2 + px + q and x^2 + mx + n, then prove that a = (n-q) / (m-p).
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If x%2Ba is a factor in
f%28x%29=x%5E2+%2B+px+%2B+q and in
g%28x%29=x%5E2+%2B+mx+%2B+n, then
f%28-a%29=a%5E2+-pa%2B+q=0 and
g%28-a%29=a%5E2+-+ma+%2B+n=0.
That would give as a system of equations that looks confusing, but we only need to solve it partially.
system%28a%5E2+-pa%2B+q=0%2Ca%5E2+-+ma+%2B+n=0%29 --> a%5E2+-pa%2B+q=a%5E2+-+ma+%2B+n --> -pa%2B+q=-+ma+%2B+n --> -pa%2B+q%2Bma=n --> -pa%2Bma=n-q --> ma-pa=n-q --> +%28m-p%29a=n-q --> highlight%28a=%28n-q%29%2F%28m-p%29%29