Solve the given two equations and select the correct answer from the given options.
$I. x = \sqrt{1764}$
$II. y^2 = 1764$

Let $\alpha$ and $\beta$ be two roots of the equation $x^2 + 2x + 2 = 0$. Then,$\alpha^{15} + \beta^{15}$ is equal to:

The number of integral values of $m$ for which the equation $(1 + m^2) x^2 - 2(1 + 3m) x + (1 + 8m) = 0$ has no real root is

If $x$ is real,the maximum value of $\frac{3x^2 + 9x + 17}{3x^2 + 9x + 7}$ is

Solve the given two equations and select the correct answer from the given options.
$I.$ $\sqrt{1225} x + \sqrt{4900} = 0$
$II.$ $(81)^{1/4} y + (343)^{1/3} = 0$

Let $\alpha, \beta$ be the roots of the quadratic equation $x^2 + px + p^3 = 0$ $(p \neq 0)$. If $(\alpha, \beta)$ is a point on the parabola $y^2 = x$,then the roots of the quadratic equation are: