Question

Find the relationship between p and q if px*2+2x-q is a perfect square. please help me ASAP​

Answer 1

`\displaystyle\\Answer:\ p=-(1)/(q)`

Explanation:

A perfect square has equal sides

Hence, px²+2x-q has equal roots (D(discriminant)=0)

`\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\\eq 0):\\-(1)/(q)=p\\ Thus,\\p=-(1)/(q)`