# What is a rational zero?

Dec 28, 2015

A rational zero of a polynomial $f \left(x\right)$ in a variable $x$ is a fraction $\frac{p}{q}$ such that $f \left(\frac{p}{q}\right) = 0$ where $p$ and $q$ are integers.

#### Explanation:

A rational number is a number that can be expressed in the form $\frac{p}{q}$ for some integers $p$ and $q$.

A zero of an expression $f \left(x\right)$ is a value of $x$ such that $f \left(x\right) = 0$.

So a rational zero of an expression $f \left(x\right)$ is basically a fraction $\frac{p}{q}$ such that $f \left(\frac{p}{q}\right) = 0$.

For example, $2 {x}^{2} - 3 x - 5$ has rational zeros $x = - 1$ and $x = \frac{5}{2}$, since substituting either of these values for $x$ in the expression results in the value $0$.