Question

How do you find the roots, real and imaginary, of `y=(x-2)(-5x+1)-x` using the quadratic formula?

Answer 1

`x=1+-sqrt(60)/10`

Explanation:

First convert the given equation into standard form:

`y=(x-2)(-5x+1)-x`

`color(white)("XXX")rArr y=-5x^2+10x-2`

For the general standard quadratic:
`color(white)("XXX")y=ax^2+bx+c`
the roots are given by the quadratic formula
`color(white)("XXX")x=(-b+-sqrt(b^2-4ac))/(2a)`

In this case
`color(white)("XXX")x=(-10+-sqrt(10^2-4(-5)(-2)))/(2(-5))`

`color(white)("XXX")x=1+-sqrt(60)/10`