Solve the given two equations and choose the correct option.
$I. 20 x^{2}-67 x+56=0$
$II. 56 y^{2}-67 y+20=0$

Solve the given two equations and select the correct answer from the given options.
$I.$ $x^{4} - 227 = 398$
$II.$ $y^{2} + 321 = 346$

Consider the equation $x^2 + \alpha x + \beta = 0$ having roots $\alpha, \beta$ such that $\alpha \neq \beta$. Also consider the inequality $| |y - \beta| - \alpha | < \alpha$,then:

If $a, b, c$ are in $G.P.$,then the equations $ax^2 + 2bx + c = 0$ and $dx^2 + 2ex + f = 0$ have a common root if $\frac{d}{a}, \frac{e}{b}, \frac{f}{c}$ are in

The roots of the equation $3 a^{2} x^{2}-a b x-2 b^{2}=0$ are

If $\alpha \ne \beta$ but $\alpha^2 = 5\alpha - 3$ and $\beta^2 = 5\beta - 3$,then the equation whose roots are $\alpha/\beta$ and $\beta/\alpha$ is