Solve the given two equations and select the correct answer from the given options.
$I.$ $2x^2 + 3x - 20 = 0$
$II.$ $2y^2 + 19y + 44 = 0$

Let $a, b \in R, a \neq 0$ be such that the equation $a x^{2}-2 b x+5=0$ has a repeated root $\alpha,$ which is also a root of the equation $x^{2}-2 b x-10=0$. If $\beta$ is the other root of this equation,then $\alpha^{2}+\beta^{2}$ is equal to

If $1 - i$ is a root of the equation ${x^2} - ax + b = 0$, then $b = $

If $\left\{\frac{1}{2}(a-b)\right\}^{2}+a b=p(a+b)^{2},$ then the value of $p$ is (assume that $a \neq-b).$

If the equation $(m - n)x^2 + (n - l)x + l - m = 0$ has equal roots,then $l, m$ and $n$ satisfy:

If $x = \frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}$ and $y = \frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}$,then the value of $\frac{x^{2}+xy+y^{2}}{x^{2}-xy+y^{2}} = ?$