Question

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

Answer 1

Roots are `-i3sqrt2` and `i3sqrt2`

Explanation:

`y=(x+2)^2-4x+14`

= `x^2+4x+4-4x+14`

= `x^2+18`

= `x^2-(isqrt18)^2`

= `(x+isqrt18)(x-isqrt18)`

= `(x+i3sqrt2)(x-i3sqrt2)`

Hence roots are `-i3sqrt2` and `i3sqrt2`