Question 857219
This requires discriminant equal to zero.


{{{Discriminant=(4q)^2-4*(p^2)*25=0}}}
{{{(4q-10p)(4q+10p)=0}}}
{{{(2q-5p)(2q+5p)=0}}}
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One or the other of each binomial factor is zero for the product to be zero.
If {{{2q-5p=0, then 2q=5p}}}
{{{5p=2q}}}
{{{5p/q=2}}}
{{{highlight(p/q=2/5)}}}--------THE ANSWER
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If {{{2q+5p=0}}}, then {{{2q=-5p}}}
{{{5p=-2q}}}
{{{5p/q=-2}}}
{{{p/q=-2/5}}} -----Which we do NOT want because it is contrary to the specifications.