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| Math Central | Quandaries & Queries |
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Question from Manashi, a student: My question is: If p,q,r be any odd integers, then prove that the roots of the quadratic equation px^2+qx+r=0 can't be rational . |
Manashi,
Try working backwards, Manashi.
A quadratic with rational roots is factored as (ax + b)(cx + d) = px2 + qx + r.
Thus, ac = p, bd = r and (ad+bc) = q.
You know that p=ac is odd, so both a and c are odd.
What can you conclude from ac = p, bd = r and (ad+bc) = q?
Cheers,
Stephen La Rocque
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