Find the set of values of the constant $p$ for which the curve $y=px^2+(p-2)x+5$ lies entirely a

Question

Find the set of values of the constant $p$ for which the curve $y=px^2+(p-2)x+5$ lies entirely above the $x$-axis.[5]

Accepted Answer

$12-2\sqrt{35}<p<12+2\sqrt{35}$

2025 JVSS PRELIMS P1 Q2