The least integer $k$ which makes the roots of the equation ${x^2} + 5x + k = 0$ imaginary is

The roots of the equation $4^x - 3 \cdot 2^{x+2} + 32 = 0$ are

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.

Solve the given two equations and select the correct answer from the given options.
$I.$ $17 x^{2}+48 x=9$
$II.$ $13 y^{2}=32 y-12$

Let one root of $ax^2 + bx + c = 0$,where $a, b, c$ are integers,be $3 + \sqrt{5}$. Then the other root is:

If $\alpha$ and $\beta$ are the roots of the equation $lx^2 + mx + n = 0$,then the equation whose roots are $\alpha^3\beta$ and $\alpha\beta^3$ is: