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

If $x^{2}-3x+1=0$,then the value of $\frac{x^{6}+x^{4}+x^{2}+1}{x^{3}}$ is:

Let $f(x)$ be a quadratic polynomial such that $f(-1)+f(2)=0$. If one of the roots of $f(x)=0$ is $3$,then its other root lies in

Solve the given two equations and select the correct answer from the given options.
$I.$ $2x^2 + 3x - 20 = 0$
$II.$ $2y^2 + 19y + 44 = 0$

If $x^{2}+y^{2}+z^{2}=2(x+z-1)$,then find the value of $x^{3}+y^{3}+z^{3}$.

Let $\alpha, \beta$ be the roots of the equation $ax^2 + 2bx + c = 0$ and $\gamma, \delta$ be the roots of the equation $px^2 + 2qx + r = 0$. If $\alpha, \beta, \gamma, \delta$ are in $G.P.$,then