# How do you write a polynomial equation of least degree given the roots -5,7?

Aug 9, 2017

$y = {x}^{2} - 2 x - 35$

#### Explanation:

$\text{given the roots are "x=-5" and } x = 7$

$\text{then the factors are "(x+5)" and } \left(x - 7\right)$

$\text{the polynomial is then the product of the factors}$

$\Rightarrow y = \left(x + 5\right) \left(x - 7\right)$

$\textcolor{w h i t e}{\Rightarrow y} = {x}^{2} - 2 x - 35 \leftarrow \textcolor{red}{\text{ of degree 2}}$