What are the x-intercept(s) of y =-x^2-2x+5?

Oct 27, 2015

x-intercepts: $x = \sqrt{6} - 1$ and $x = - \sqrt{6} - 1$

Explanation:

The x-intercepts are the values of $x$ when $y = 0$ (the line of the graph crosses the X-axis when $y = 0$)

$y = - {x}^{2} - 2 x + 5 = 0$

$\Rightarrow {x}^{2} + 2 x - 5 = 0$

$\textcolor{w h i t e}{\text{XXX}} x = \frac{- 2 \pm \sqrt{{2}^{2} - 4 \left(1\right) \left(- 5\right)}}{2 \left(1\right)}$
$\textcolor{w h i t e}{\text{XXXX}} = \frac{- 2 \pm \sqrt{24}}{2}$
$\textcolor{w h i t e}{\text{XXXX}} = \frac{- 2 \pm 2 \sqrt{6}}{2}$
$\textcolor{w h i t e}{\text{XXXX}} = - 1 \pm \sqrt{6}$