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Math Help - help with proof.

  1. #1
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    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)
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by jeffjohnson View Post
    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
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