The quadratic equation whose roots are the numbers having arithmetic mean $34$ and geometric mean $16$ is

If the roots of the equations $px^2 + 2qx + r = 0$ and $qx^2 - 2\sqrt{pr}x + q = 0$ are real,then .........

The quadratic equation whose one root is $\frac{1}{2 + \sqrt{5}}$ will be

Consider the following two statements:
$I$. Any pair of consistent linear equations in two variables must have a unique solution.
$II$. There do not exist two consecutive integers,the sum of whose squares is $365$.
Then,

The expression $ax^{2} + bx + c$ (where $a, b,$ and $c$ are real numbers) has the same sign as that of $a$ for all $x \in \mathbb{R}$ if:

The sum of the non-real roots of $(p^2+p-3)(p^2+p-2)-12=0$ is