# Thread: help with proof.

1. ## help with proof.

Prove that if one solution of a quadratic equation of the form x^2+bx+c=0 is rational(where b and c are rational) then the other solution is also rational. Use the fact that if the solutions of the equation are r and s, then
x^2+bx+c = (x-r)(x-s)

2. Originally Posted by jeffjohnson
Prove that if one solution of a quadratic equation of the form x^2+bx+c=0 is rational(where b and c are rational) then the other solution is also rational. Use the fact that if the solutions of the equation are r and s, then
x^2+bx+c = (x-r)(x-s)
$\left(x-\frac{p}{q}\right)\left(x-c\right)=x^2-{\color{red}\left(c+\frac{p}{q}\right)}x+c\frac{p} {q}=x^2+{\color{red}b}x+c$