Solve the given two equations and select the correct answer from the given options.
$I.$ $x^{2}-24x+144=0$
$II.$ $y^{2}-26y+169=0$

If the sum of the roots of the equation $ax^2 + bx + c = 0$ is equal to the sum of their squares,then:

The coefficient of $x$ in the equation $x^2 + px + q = 0$ was taken as $17$ in place of $13$. Its roots were found to be $-2$ and $-15$. The roots of the original equation are:

The quadratic equation whose one root is $\frac{1}{2 + \sqrt{5}}$ will be

If $\log_2 x + \log_x 2 = \frac{10}{3} = \log_2 y + \log_y 2$ and $x \neq y$,then $x + y = $

The value of $k$ for which the roots $\alpha, \beta$ of the equation $x^{2}-6x+k=0$ satisfy the relation $3\alpha+2\beta=20$ is: