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

1 Answer
Alan P.
Jun 5, 2016

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

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