Let $a, b, c, p, q$ be real numbers. Suppose $\alpha, \beta$ are the roots of the equation $x^2+2 p x+q=0$ and $\alpha, \frac{\beta}{2}$ are the roots of the equation $a x^2+2 b x+c=0$, where $\beta^2 \notin\{-1,0,1\}$.
STATEMENT-1: $\left(\mathrm{p}^2-\mathrm{q}\right)\left(\mathrm{b}^2-\mathrm{ac}\right) \geq 0$
and
STATEMENT-2: $\quad \mathrm{b} \neq \mathrm{pa}$ or $\mathrm{c} \neq \mathrm{qa}$
$\& \mathrm{~b} \neq \mathrm{pa}, \mathrm{c} \neq \mathrm{qa}$