# How do you write a polynomial function of least degree given the zeros -5, sqrt3?

Oct 5, 2016

$f \left(x\right) = {x}^{2} - \left(\sqrt{3} - 5\right) x - 5 \sqrt{3}$

#### Explanation:

Let's express the function as $f \left(x\right) = \left(x + 5\right) \left(x - \sqrt{3}\right)$:

$\implies f \left(x\right) = \left(x + 5\right) \left(x - \sqrt{3}\right)$

$\implies f \left(x\right) = \left(x\right) \left(x\right) + \left(x\right) \left(- \sqrt{3}\right) + \left(5\right) \left(x\right) + \left(5\right) \left(- \sqrt{3}\right)$

$\implies f \left(x\right) = {x}^{2} - \sqrt{3} x + 5 x - 5 \sqrt{3}$

$\implies f \left(x\right) = {x}^{2} - \left(\sqrt{3} - 5\right) x - 5 \sqrt{3}$