Explanation

(a)
Since, $3p^{2} = 5p + 2$
$\Rightarrow p = 2,\ - \frac{1}{3}$
And, $3q^{2} = 5q + 2\ \Rightarrow \ \ \ q = 2,\ - \frac{1}{3}$
$\because p \neq q$
Here, we assume that $p = 2$ and $q = - \frac{1}{3}$
Now, the given roots of the equation are
$(3p - 2q)$ and $(3q - 2p)ie,\ \left( \frac{20}{3},\ - 5 \right)$
Sum of roots$= \frac{20}{3} - 5 = \frac{5}{3}$
And product of roots$= \frac{20}{3} \times ( - 5) = - \frac{100}{3}$
$\therefore$ Required equation is
$x^{2} - \frac{5}{2}x - \frac{100}{3} = 0$
$\Rightarrow 3x^{2} - 5x - 100 = 0$