# How do you write a polynomial equation of least degree given the roots -2, -0.5, 4?

Sep 22, 2017

$p \left(x\right) = 2 {x}^{3} - 3 {x}^{2} - 18 x - 8$

#### Explanation:

$\text{given the roots of a polynomial are}$

$x = a , x = b , x = c , x = d$

$\text{then the factors of the polynomial are}$

$\left(x - a\right) , \left(x - b\right) , \left(x - c\right) \text{ and } \left(x - d\right)$

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

$p \left(x\right) = \left(x - a\right) \left(x - b\right) \left(x - c\right) \left(x - d\right)$

$\text{here "x=-2,x=-0.5,x=4" are the roots}$

$\Rightarrow \left(x + 2\right) , \left(x + 0.5\right) \text{ and "(x-4)" are the factors}$

$\Rightarrow p \left(x\right) = \left(x + 2\right) \left(x + 0.5\right) \left(x - 4\right)$

$\textcolor{w h i t e}{\Rightarrow p \left(x\right)} = 2 {x}^{3} - 3 {x}^{2} - 18 x - 8 \text{ possible polynomial}$