If the quadratic equation $ax^2+bx+c=0$ $(a>0)$ has two roots $\alpha$ and $\beta$ such that $\alpha < -2$ and $\beta > 2$, then which of the following is true?

If exactly one root of the equation $x^2 + (a - 1)x + 2a = 0$ lies in the interval $(0, 3)$,then the set of values of $a$ is given by:

If $\alpha$ and $\beta$ are the roots of the quadratic equation $x^2 - 3x + a = 0$,where $a \in R$ and $\alpha < 1 < \beta$,then which of the following is true?

The number of values of $k$ for which the equation $x^2 - 3x + k = 0$ has two real and distinct roots lying in the interval $(0, 1)$ is

Statement-$I$: If the roots $\alpha, \beta$ of the equation $x^2 + 2(a - 3)x + 9 = 0$,$a \in R$ satisfy $\alpha < 6 < \beta$,then $a < -3/4$.
Statement-$II$: If $f(x) = x^2 + 2(a - 3)x + 9$,then $f(6) < 0 \implies a < -3/4$.

If non-zero real numbers $p$ and $q$ exist such that $\min f(x) > \max g(x)$,where $f(x) = x^2 + 2px + 2q^2$ and $g(x) = -x^2 - 2qx + p^2$ for $x \in \mathbb{R}$,find the set of values containing $|\frac{2p}{q}|$.