# Real Zero of a Function

A real zero of a function is a real number that makes the value of the function equal to zero.

A real number, $r$ , is a zero of a function $f$ , if $f\left(r\right)=0$ .

Example:

$f\left(x\right)={x}^{2}-3x+2$

Find $x$ such that $f\left(x\right)=0$ .

$0={x}^{2}-3x+2$

$0=\left(x-2\right)\left(x-1\right)$

$x=2\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{or}\text{\hspace{0.17em}}\text{\hspace{0.17em}}x=1$

$f\left(2\right)={2}^{2}-3\left(2\right)+2=0$

$f\left(1\right)={1}^{2}-3\left(1\right)+2=0$

Since $f\left(2\right)=0$ and $f\left(1\right)=0$ , both $2$ and $1$ are real zeros of the function.