The roots of the equation ${x^4} - 8{x^2} - 9 = 0$ are

If the product of the roots of the equation $2x^2 + 6x + \alpha^2 + 1 = 0$ is $-\alpha$, then the value of $\alpha$ will be

Let $a \ne b, c \ne 0$. If the equations $x^2 + ax + bc = 0$ and $x^2 + bx + ac = 0$ have a common root,then:
Statement $-1$: The equation of the other roots is $x^2 + cx + ab = 0$.
Statement $-2$: $a + b + c = 0$.

Solve the given two equations and select the correct answer from the given options:
$I.$ $679 x^{2} - 168 x^{2} = 3066$
$II.$ $\sqrt{144} y^{3} - 9 y^{3} = 1536$

If the roots of $x^2 - 7x + 6 = 0$ are $\alpha$ and $\beta$,then $\frac{1}{\alpha} + \frac{1}{\beta} = $

Solve the given two equations and select the correct answer from the given options.
$I. 3x^2 - 4x - 32 = 0$
$II. 2y^2 - 17y + 36 = 0$