The problem states that $p$ and $q$ are the roots of the quadratic equation:

$2x^2 - 2x - 24 = 0$

We can solve for $p$ and $q$ using the quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

For the given equation, $2x^2 - 2x - 24 = 0$, we have:

• $a = 2$
• $b = -2$
• $c = -24$

Let's solve this equation using the quadratic formula.The roots of the quadratic equation $2x^2 - 2x - 24 = 0$ are:

$p = 4 \quad \text{and} \quad q = -3$

Let me know if you need further details or explanations!

Here are 5 related questions for further practice:

1. How do you factorize the equation $2x^2 - 2x - 24 = 0$?
2. What are the sum and product of the roots of this quadratic equation?
3. How would you solve this equation by completing the square?
4. What happens to the roots if we change the coefficient of $x^2$?
5. How do you derive the quadratic formula from a general quadratic equation?

Tip: Always check the discriminant first. If it's negative, the quadratic has no real roots!