Question

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

Answer 1

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=(-b+-sqrt{b^2-4ac})/(2a)`

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

`y=(x-7)^2=x^2-14x+49`

Now, just apply the QF

`x=(-(-14)+-sqrt{(-14)^2-4(1)(49)})/(2(1))`
`x=(14+-sqrt{196-196})/(2)`
`x=(14+-0)/(2)`
`x=(14)/(2)`
`x=7`

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