Originally Posted by

**HallsofIvy** What you have written is y= (4/x)+ p. Sometimes that is, incorrectly, written when a person really means y= 4/(x+ p). Can you verify which you mean?

Why are you setting y equal to 0? The problem asks for possible values of y, not p.

If y= (4/x)+ p and x= p then y= (4/p)+ p= (4+p^2)/p. If we attempt to solve that for p, we get 4+ p^2= py or p^2- py+ 4= 0. The "discriminant" from the quadratic formula is p^2- 16. p will be real if and only if $\displaystyle p^2- 16\ge 0$ or $\displaystyle p^2\ge 16$. That gives $\displaystyle p\le -4$ or $\displaystyle p\ge 4$.