# Is it possible to factor y= - x^2 - 10x + 20? If so, what are the factors?

Dec 26, 2015

It's possible to factor this polynomial in $\mathbb{R}$ as $- \left(x + 5 - 3 \sqrt{5}\right) \left(x + 5 + 3 \sqrt{5}\right)$

#### Explanation:

We need to calculate $\Delta = {b}^{2} - 4 a c$ in order to find the roots.

Here, $\Delta = 100 - 4 \cdot \left(- 1\right) \cdot 20 = 180 > 0$ so it has 2 real roots.

The quadratic formula tells us that the solutions are $\frac{- b \pm \sqrt{\Delta}}{2} a$. Here, $\sqrt{\Delta} = \sqrt{180} = 6 \sqrt{5}$

${x}_{1} = \frac{10 - 6 \sqrt{5}}{-} 2 = \frac{6 \sqrt{5} - 10}{2} = 3 \sqrt{5} - 5$ and ${x}_{2} = \frac{- 10 - 6 \sqrt{5}}{2} = - 5 - 3 \sqrt{5}$.