# What are all the zeroes of the function f(x) = x^2-169?

Mar 15, 2018

The zeroes of f(x) are $\pm$ 13

#### Explanation:

let f(x) = 0

${x}^{2}$ - 169 = 0

${x}^{2}$ = 169

take square root of both sides

sqrt${x}^{2}$ =$\pm$sqrt169

x = $\pm$13

$\therefore$The zeroes of f(x) are $\pm$13

Mar 15, 2018

$x = \pm 13$

#### Explanation:

$\text{to find the zeros set } f \left(x\right) = 0$

$\Rightarrow f \left(x\right) = {x}^{2} - 169 = 0$

$\Rightarrow {x}^{2} = 169$

$\textcolor{b l u e}{\text{take the square root of both sides}}$

$\Rightarrow x = \pm \sqrt{169} \leftarrow \textcolor{b l u e}{\text{note plus or minus}}$

$\Rightarrow x = \pm 13 \leftarrow \textcolor{b l u e}{\text{are the zeros}}$

Mar 15, 2018

$f \left(x\right)$ has exactly two zeroes: $+ 13$ and $- 13$.

#### Explanation:

We call zero of a function to those values of $x$ such that $f \left(x\right) = 0$. We call also roots in polynomial functions.

In our case, we have to resolve ${x}^{2} - 169 = 0$

Transposing terms, we have ${x}^{2} = 169$. the square root of both sides give us

$\sqrt{{x}^{2}} = x = \pm \sqrt{169} = \pm 13$ because

(+13)·(+13)=13^2=169 and
(-13)·(-13)=(-13)^2=169