How do you find the roots, real and imaginary, of y=(x – 7 )^2 using the quadratic formula?

May 2, 2017

First off, we really don't need the quadratic formula to find all the roots here since it's already factored, but I'll use it anyway.

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

We need your equation in standard form to use the QF. I'm assuming you know how to do this.

$y = {\left(x - 7\right)}^{2} = {x}^{2} - 14 x + 49$

Now, just apply the QF

$x = \frac{- \left(- 14\right) \pm \sqrt{{\left(- 14\right)}^{2} - 4 \left(1\right) \left(49\right)}}{2 \left(1\right)}$
$x = \frac{14 \pm \sqrt{196 - 196}}{2}$
$x = \frac{14 \pm 0}{2}$
$x = \frac{14}{2}$
$x = 7$

That's the only root it has. There are no imaginary roots for this quadratic.