Question

let's see who can solve this

Answer 1

The roots of a quadratic equation is real if it's discriminant is >= 0. So,
${ (- 4)}^{2} - 4 \times 1 \times - log_{3}(p) \geqslant 0 \\ 16 + 4 log_{3}(p) \geqslant 0 \\ log_{3}(p) \geqslant - 4 \\ p \geqslant {3}^{ - 4} \\ therefore \: minimum \: value \: of \: p \\ is \: \: p = {3}^{ - 4} = \frac{1}{81}$
Option (c)