tangyecomfort333
tangyecomfort333 tangyecomfort333
  • 22-09-2022
  • Mathematics
contestada

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

Respuesta :

sangers1959 sangers1959
  • 22-09-2022

[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]

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