# How do you find all the zeros of f(x) = -3(x+1/2)(x-4)^3?

Mar 2, 2016

$x = - \frac{1}{2}$ and $x = 4$

#### Explanation:

if you have a product of several factors, and their product is zero is because at least one of them is zero:

Symbolically:

$a b c \mathrm{de} f = 0 \implies a = 0 \mathmr{and} b = 0 \mathmr{and} c = 0 \mathmr{and} d = 0 \mathmr{and} e = 0 \mathmr{and} f = 0$

So the zeros of $- 3 \left(x + \frac{1}{2}\right) {\left(x - 4\right)}^{3}$

can be calculted by solving:

$x + \frac{1}{2} = 0$ and $x - 4 = 0$

$x = - \frac{1}{2}$ and $x = 4$