Solve the given two equations and select the correct answer from the given options.
$I.$ $5x^{2} + 2x - 3 = 0$
$II.$ $2y^{2} + 7y + 6 = 0$

Solve the given two equations and select the correct option.
$I.$ $36 x^{2}+47 \sqrt{7} x+105=0$
$II.$ $35 y^{2}+20 \sqrt{3} y+63 \sqrt{2} y+36 \sqrt{6}=0$

The quadratic equations $x^2 - 6x + a = 0$ and $x^2 - cx + 6 = 0$ have one root in common. The other roots of the first and second equations are integers in the ratio $4 : 3$. Then the common root is:

If $\alpha$ and $\beta$ are the roots of the equation $x^{2}+3ax+c=0$ and if $\alpha^{2}+\beta^{2}=5$,find the value of $a$.

Let $\alpha, \beta$ be the roots of $x^2 - x + p = 0$ and $\gamma, \delta$ be the roots of $x^2 - 4x + q = 0$. If $\alpha, \beta, \gamma, \delta$ are in $G.P.$,then the integral values of $p, q$ are respectively:

With respect to the roots of $x^{2}-x-2=0$,we can say that