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

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Answer 1 · 2017-05-02T14:54:13

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.

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