Solve the given two equations and select the correct answer from the given options.
$I.$ $7x^2 + 16x - 15 = 0$
$II.$ $y^2 - 6y - 7 = 0$

If $\lambda$ is the ratio of the roots of the quadratic equation in $x$,$3m^2x^2 + m(m - 4)x + 2 = 0$,then the least value of $m$ for which $\lambda + \frac{1}{\lambda} = 1$ is:

Solve the given two equations and select the correct option.
$I.$ $2x^2 + 23x + 63 = 0$
$II.$ $4y^2 + 19y + 21 = 0$

$I. x^{2}+10 x+24=0$
$II. 4 y^{2}-17 y+18=0$

Two candidates attempt to solve the equation $x^2 + px + q = 0$. One starts with a wrong value of $p$ and finds the roots to be $2$ and $6$,and the other starts with a wrong value of $q$ and finds the roots to be $2$ and $-9$. The roots of the original equation are

Solve the given two equations and select the correct answer from the given options.
$I.$ $\frac{15}{\sqrt{x}} - \frac{9}{\sqrt{x}} = (x)^{1/2}$
$II.$ $y^{10} - (36)^{5} = 0$