# help with proof.

• February 21st 2010, 07:44 PM
jeffjohnson
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)
• February 21st 2010, 07:46 PM
Drexel28
Quote:

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)

$\left(x-\frac{p}{q}\right)\left(x-c\right)=x^2-{\color{red}\left(c+\frac{p}{q}\right)}x+c\frac{p} {q}=x^2+{\color{red}b}x+c$