# How do you use the quadratic formula to solve for x-intercepts x^2 − 5x − 3 = 0?

Jun 13, 2017

$x \approx 5.54138 \mathmr{and} \approx - 0.54138$

#### Explanation:

The quadratic formula states that for a quadratic equation of standard form $\left(a {x}^{2} + b x + c = 0\right)$ it's roots are given by:

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

In this example we are asked to find the x-intercepts (which are the roots) of ${x}^{2} - 5 x - 3 = 0$

$\therefore a = 1 , b = - 5 , c = - 3$

Hence $x = \frac{- \left(- 5\right) \pm \sqrt{{\left(- 5\right)}^{2} - 4 \cdot 1 \cdot \left(- 3\right)}}{2 \cdot 1}$

$= \frac{5 \pm \sqrt{25 + 12}}{2}$

$= \frac{5 \pm \sqrt{37}}{2}$

$x \approx 5.54138 \mathmr{and} \approx - 0.54138$

These x-intercepts can be seen on the graph of this quadratic below

graph{x^2-5x-3 [-18.14, 22.4, -9.91, 10.36]}