Solve the given two equations and select the correct option.
$I.$ $9x^{2} - 114x + 361 = 0$
$II.$ $y^{2} = 36$

The roots of the given equation $2(a^2 + b^2)x^2 + 2(a + b)x + 1 = 0$ are

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:

Solve the given two equations and select the correct answer from the given options.
$I.$ $\sqrt{784} x + 1234 = 1486$
$II.$ $\sqrt{1089} y + 2081 = 2345$

If $c > 0$ and the equation $3ax^2 + 4bx + c = 0$ has no real root,then :-

Solve the given two equations and select the correct answer from the given options.
$I.$ $12 x^{2} + 11 x - 56 = 0$
$II.$ $4 y^{2} - 15 y + 14 = 0$