If the roots of the equation $5x^2 - 7x + k = 0$ are reciprocals of each other,then the value of $k$ is:

The roots of the equation $a^{2} x^{2}-3 a b x+2 b^{2}=0$ are

Solve the given two equations and select the correct answer from the given options.
$I.$ $x^{2}+13x+40=0$
$II.$ $y^{2}+7y+10=0$

Solve the given two equations and select the correct answer from the given options.
$I.$ $x^{2}-7x+12=0$
$II.$ $y^{2}+y-12=0$

Solve the given two equations and provide the correct answer from the given options.
$I.$ $3x^2 - (6 + \sqrt{17})x + 2\sqrt{17} = 0$
$II.$ $5y^2 - (15 - \sqrt{17})y - 3\sqrt{17} = 0$

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