# If p and q are distinct real numbers that satisfy the equation 3y^2-11y-224=0, find the sum of p + q?

## 3y^2 - 11y - 224 = 0

Feb 25, 2017

$\left(p + q\right) = \frac{11}{3}$

#### Explanation:

We have

$3 {p}^{2} - 11 p - 224 = 0$ and

$3 {q}^{2} - 11 q - 224 = 0$

subtracting term to term

$3 \left({p}^{2} - {q}^{2}\right) - 11 \left(p - q\right) = 0$ or

$\left(3 \left(p + q\right) - 11\right) \left(p - q\right) = 0$

now supposing that $p \ne q$ we have

$3 \left(p + q\right) - 11 = 0 \to \left(p + q\right) = \frac{11}{3}$