# How do you find the roots, real and imaginary, of y= x^2 - 8x + 15  using the quadratic formula?

Dec 6, 2015

Apply the quadratic formula to find that the roots are $x = 3$ and $x = 5$.

#### Explanation:

$a {x}^{2} + b x + c = 0 \implies x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$
Note that the solutions to $x$ for the initial equation are the roots of
$f \left(x\right) = a {x}^{2} + b x + c$.

Applying that here, we get
${x}^{2} - 8 x + 15 = 0$

$\implies x = \frac{- \left(- 8\right) \pm \sqrt{{\left(- 8\right)}^{2} - 4 \left(15\right) \left(1\right)}}{2 \left(1\right)}$

$= \frac{8 \pm \sqrt{4}}{2}$

$= 4 \pm 1$

Thus the roots are $x = 3$ and $x = 5$.