# How do you find the roots, real and imaginary, of y= x^2 + 4x - 1  using the quadratic formula?

Jul 29, 2016

$\left\{- 2 - \sqrt{5} , - 2 + \sqrt{5}\right\}$

#### Explanation:

$a {x}^{2} + b x + c = 0$

we have

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

Then, with ${x}^{2} + 4 x - 1 = 0$, we have $a = 1 , b = 4 , c = - 1$. Applying the formula gives us

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

$= \frac{- 4 \pm \sqrt{20}}{2}$

$= \frac{- 4 \pm 2 \sqrt{5}}{2}$

$= - 2 \pm \sqrt{5}$

Thus the two roots of the given equation are $- 2 + \sqrt{5}$ and $- 2 - \sqrt{5}$