Solve the given two equations and select the correct answer from the given options.
$I.$ $17 x^{2}+48 x=9$
$II.$ $13 y^{2}=32 y-12$

If the roots of the equation $bx^2 + cx + a = 0$ are imaginary,then for all real values of $x$,the expression $3b^2x^2 + 6bcx + 2c^2$ is:

If $\alpha_1 < \alpha_2 < \alpha_3 < \alpha_4 < \alpha_5 < \alpha_6$,then the equation $(x - \alpha_1)(x - \alpha_3)(x - \alpha_5) + 3(x - \alpha_2)(x - \alpha_4)(x - \alpha_6) = 0$ has :-

If $a < 0$,then the inequality $ax^2 - 2x + 4 > 0$ has the solution represented by:

In the following,determine the set of values of $P$ for which the given quadratic equation $Px^2 + 4x + 1 = 0$ has real roots.

If the roots of the given equation $(\cos p - 1)x^2 + (\cos p)x + \sin p = 0$ are real,then