The roots of the equation $ix^2 - 4x - 4i = 0$ are

If the equations $x^{2}+2x-3=0$ and $x^{2}+3x-k=0$ have a common root,then the non-zero value of $k$ is:

If $x = \sqrt {1 + \sqrt {1 + \sqrt {1 + \dots \infty} } }$,then $x =$

The roots of the equation $4x^4 - 24x^3 + 57x^2 + 18x - 45 = 0$ are given. If one of the roots is $3 + i\sqrt{6}$, find the other roots.

If $\left(\frac{p^{-1} q^{2}}{p^{3} q^{-2}}\right)^{\frac{1}{3}}+\left(\frac{p^{5} q^{-3}}{p^{-2} q^{3}}\right)^{\frac{1}{3}}=p^{a} q^{b},$ then the value of $a+b,$ where $p$ and $q$ are different positive positive primes,is

Solve the given two equations and select the correct answer from the given options.
$I.$ $8x^2 + 6x = 5$
$II.$ $12y^2 - 22y + 8 = 0$