Question

How do you find the roots, real and imaginary, of `y= x^2 + 8x -9- (-x-1)^2` using the quadratic formula?

Answer 1

x=5/3

Explanation:

There are no imaginary roots of this equation.
To get the roots, put y=0
Now expand `(-x-1)^2` which is actually `(x+1)^2`

`x^2+8x-9-(x^2+2x+1)=0`

`cancel(x^2)+8x-9cancel(-x^2)-2x-1=0`

`6x-10=0`

`x=5/3`

Additionally you can also see that this equation is actually equation of a straight line so it can have at most 1 zero (which is real).