# How do I find all the rational zeros of function?

Jan 27, 2015

To find the zeroes of a function, $f \left(x\right)$, set $f \left(x\right)$ to zero and solve.
For polynomials, you will have to factor.

For example: Find the zeroes of the function $f \left(x\right) = {x}^{2} + 12 x + 32$

First, because it's a polynomial, factor it
$f \left(x\right) = \left(x + 8\right) \left(x + 4\right)$

Then, set it equal to zero
$0 = \left(x + 8\right) \left(x + 4\right)$

Set each factor equal to zero and the answer is $x = - 8$ and $x = - 4$.

*Note that if the quadratic cannot be factored using the two numbers that add to this and multiple to be this method, then use the quadratic formula $\frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

to factor an equation in the form of $a {x}^{2} + b x + c$.