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

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