# How do you write a polynomial with zeros 2, 4+sqrt5,  4-sqrt5?

Feb 7, 2016

#### Answer:

${x}^{3} - 10 {x}^{2} + 27 x - 22$

#### Explanation:

The polinonimal will be the result of

$\left(x - 2\right) \left(x - 4 - \sqrt{5}\right) \left(x - 4 + \sqrt{5}\right)$

$\left(x - 2\right) \left({\left(x - 4\right)}^{2} - 5\right)$

$\left(x - 2\right) \left({x}^{2} - 8 x + 16 - 5\right)$

$\left(x - 2\right) \left({x}^{2} - 8 x + 11\right)$

${x}^{3} - 8 {x}^{2} + 11 x - 2 {x}^{2} + 16 x - 22$

${x}^{3} - 10 {x}^{2} + 27 x - 22$ or a multiple of it:

$a \left({x}^{3} - 10 {x}^{2} + 27 x - 22\right)$