If one root of $5x^2 + 13x + k = 0$ is the reciprocal of the other,then $k = $

If the product of the roots of the equation ${x^2} - 3kx + 2{e^{2\log k}} - 1 = 0$ is $7$,then for what value of $k$ will its roots be real?

Solve the given two equations and select the correct answer from the given options.
$I.$ $3x^2 - 7x - 20 = 0$
$II.$ $y^2 - 8y + 16 = 0$

Solve the given two equations and select the correct answer from the given options.
$I.$ $\frac{9}{\sqrt{x}} + \frac{19}{\sqrt{x}} = \sqrt{x}$
$II.$ $y^{5} - \frac{(28)^{1/2}}{\sqrt{y}} = 0$

The equation formed by decreasing each root of $ax^2 + bx + c = 0$ by $1$ is $2x^2 + 8x + 2 = 0$. Then:

$x=3$ is a solution of the equation $3x^{2} + (k-1)x + 9 = 0$ if $k$ has the value: