[tex]\displaystyle\\Answer:\ p=-\frac{1}{q}[/tex]
Step-by-step explanation:
A perfect square has equal sides
Hence, px²+2x-q has equal roots (D(discriminant)=0)
[tex]\displaystyle\\D=2^4-4*p*(-q)\\D=2*2+4pq\\D=4+4pq\\D=0\\\Rightarrow\ 0=4+4pq\\Divide\ both\ parts\ of\ the \ equation\ by\ 4:\\0=1+pq\\0-1=1+pq-1\\-1=pq\\Divide\ both\ parts\ of\ the \ equation\ by\ q(q\neq 0):\\-\frac{1}{q}=p\\ Thus,\\p=-\frac{1}{q}[/tex]
