The problem asks us to find the quadratic equation whose roots are $-2q$ and $5q$.

1. Problem Description

The problem asks us to find the quadratic equation whose roots are $-2q$ and $5q$.

2. Solution Steps

A quadratic equation with roots $r_1$ and $r_2$ can be written in the form:

$x^2 - (r_1 + r_2)x + r_1r_2 = 0$

In our case, $r_1 = -2q$ and $r_2 = 5q$.

First, find the sum of the roots:

$r_1 + r_2 = -2q + 5q = 3q$

Next, find the product of the roots:

$r_1r_2 = (-2q)(5q) = -10q^2$

Substitute these values into the quadratic equation formula:

$x^2 - (3q)x + (-10q^2) = 0$

$x^2 - 3qx - 10q^2 = 0$

3. Final Answer

The quadratic equation is $x^2 - 3qx - 10q^2 = 0$. Therefore, the answer is D.