Number of integral values of $a$ for which both roots of the quadratic equation $x^2 - (2a + 3)x + a^2 + 3a = 0$ lie in the interval $(0, 4)$ is:

If $a(p + q)^2 + 2bpq + c = 0$ and $a(p + r)^2 + 2bpr + c = 0$,then $qr$ =

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.

If one root of the quadratic equation $ax^2 + bx + c = 0$ is equal to the $n^{th}$ power of the other root,then the value of $(ac^n)^{\frac{1}{n+1}} + (a^nc)^{\frac{1}{n+1}} = $

The number of real solutions of the equation $|x^2 + 4x + 3| + 2x + 5 = 0$ is:

Solve the given two equations and select the correct answer from the given options.
$I.$ $2x^{2} + 11x + 14 = 0$
$II.$ $4y^{2} + 12y + 9 = 0$