$A$ two-digit number is four times the sum of its digits and three times the product of its digits. The number is:

If $\alpha$ and $\beta$ are two real numbers satisfying $\alpha^2 + \beta^2 = 5$ and $3(\alpha^5 + \beta^5) = 11(\alpha^3 + \beta^3)$,then the value of $\alpha \beta$ is:

Let $p, q, r \in \mathbb{R}$ and $r > p > 0.$ If the quadratic equation $px^2 + qx + r = 0$ has two complex roots $\alpha$ and $\beta,$ then $|\alpha| + |\beta|$ is:

Number of integral values of $m$ for which ${x}^2 + 5m{x} - 3m + 1 < 0$ $\forall x \in R$ is (where ${.}$ denotes the fractional part function).

Solve the given two equations and select the correct answer from the given options.
$I.$ $x^{2}+12x+36=0$
$II.$ $y^{2}+15y+56=0$

Find two consecutive positive odd integers whose squares have the sum $290.$