# How do you find the zeros by rewriting the function y=x^2-10x+24 in intercept form?

May 8, 2017

$x = 4 , x = 6$

#### Explanation:

$\text{factorise } {x}^{2} - 10 x + 24$

$\text{consider factors of the product 24 that sum to - 10}$

$\text{the factors are - 4 and - 6}$

$\Rightarrow y = \left(x - 4\right) \left(x - 6\right)$

$\text{zeros are the values of x that make y = 0}$

$\text{solve } \left(x - 4\right) \left(x - 6\right) = 0$

$x - 4 = 0 \Rightarrow x = 4 \leftarrow \textcolor{red}{\text{ is a zero}}$

$x - 6 = 0 \Rightarrow x = 6 \leftarrow \textcolor{red}{\text{ is a zero}}$