Math CentralQuandaries & Queries


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 .


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?

Stephen La Rocque


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