# How do you find the roots, real and imaginary, of y=(x +2 )^2-4x+14 using the quadratic formula?

Feb 11, 2018

Roots are $- i 3 \sqrt{2}$ and $i 3 \sqrt{2}$

#### Explanation:

$y = {\left(x + 2\right)}^{2} - 4 x + 14$

= ${x}^{2} + 4 x + 4 - 4 x + 14$

= ${x}^{2} + 18$

= ${x}^{2} - {\left(i \sqrt{18}\right)}^{2}$

= $\left(x + i \sqrt{18}\right) \left(x - i \sqrt{18}\right)$

= $\left(x + i 3 \sqrt{2}\right) \left(x - i 3 \sqrt{2}\right)$

Hence roots are $- i 3 \sqrt{2}$ and $i 3 \sqrt{2}$