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If p, q and r are odd integers then prove that the roots of px^2+qx+r cannot be rational.

If p, q and r are odd integers then prove that the roots of px^2+qx+r cannot be rational.

Grade:12

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
6 years ago
Hello student,
Please find the answer to your question
Let us assume that px2+qx+r=0 has rational roots
then let (ax+b)(cx+d)=px2+qx+r
then ac=p ;ad+bc=q and bd=r
if p and r are odd
then since ac=p and bd=r
we can say a,c and b,d are also odd
ad+bc=odd+odd=even
so q=ad+bc is even
so all cannot be odd when roots are rational
Hence if p,q,r are odd then roots of px2+qx+r cannot be rational

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