Question

How do you find the roots, real and imaginary, of `y=-5(x-3)^2-(x-3)^2-10` using the quadratic formula?

Answer 1

`3-i10sqrt2` and `3+i10sqrt2` are roots of given equation.

Explanation:

For equation `ax^2+bx+c=0`, quadratic formula gives `x=(-b+-sqrt(b^2-4ac))/(2a)`.

In equation `y=-5(x-3)^2-(x-3)^2-10=-6(x-3)^2-10`. Hence, `(x-3)=(0+-sqrt(0^2-4(-5)(-10)))/(2xx(-5))=(+-sqrt(-200))/(-10)=+-i10sqrt2/(-10)=+-i10sqrt2`

Hence, `x=3+-i10sqrt2` and these are roots of given equation.