Repeated Zeros

The zeros arising from repeated factors of a polynomial function are called repeated zeros .

Example:

$f\left(x\right)={x}^{2}-6x+9$

Set $f\left(x\right)$ to zero, factor and solve.

$0=\left(x-3\right)\left(x-3\right)$

$x=3\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{or}\text{\hspace{0.17em}}\text{\hspace{0.17em}}x=3$

Since $x-3$ appears twice as a factor, $3$ appears twice as a zero of the function and is called a repeated zero of the function.