# Which of the following are the coordinates of the roots of -4x^2 - 32x - 60 = 0?

Jun 24, 2015

Assuming that the question only really meant to ask for the roots of the given equation:
the roots are $\left\{- 3 , - 5\right\}$

#### Explanation:

$- 4 {x}^{2} - 32 x - 60 = 0$
is equivalent to (after dividing both sides by $\left(- 4\right)$
$\textcolor{w h i t e}{\text{XXXX}}$${x}^{2} + 8 x + 15 = 0$
The left side can be factored to give
$\textcolor{w h i t e}{\text{XXXX}}$$\left(x + 3\right) \left(x + 5\right) = 0$
Which implies
$\textcolor{w h i t e}{\text{XXXX}}$$\left(x + 3\right) = 0$ or $\left(x + 5\right) = 0$

Which, in turn implies
either $x = - 3$ or $x = - 5$