Solve the given two equations and select the correct answer from the given options.
$I.$ $x^{2}-6x=7$
$II.$ $2y^{2}+13y+15=0$

Solve the given two equations and select the correct option.
$I.$ $x^{2} + 42 = 13x$
$II.$ $y = \sqrt[4]{1296}$

If $\alpha, \beta$ are the roots of $(x - a)(x - b) = c,$ where $c \neq 0,$ then the roots of $(x - \alpha)(x - \beta) + c = 0$ are

The product of all real roots of the equation ${x^2} - |x| - 6 = 0$ is

Let $\alpha, \beta, \gamma, \delta$ be the roots of the equation $x^4 + x^2 + 1 = 0$. Then,the equation whose roots are $\alpha^2, \beta^2, \gamma^2, \delta^2$ is:

Babu starts from his house at a certain time with a certain speed to pick up his girlfriend from the office at $5:00 \, PM$. One day,his girlfriend left the office at $3:00 \, PM$ and started walking home at a speed of $40 \, km/h$. She met Babu on the way,who had left his home at his usual time. They reached home $40 \, min$ earlier than their usual time. If Quantity $I$ is the speed of Babu and Quantity $II$ is $120 \, km/h$,compare the two quantities.