How do you find the roots, real and imaginary, of y=3x^2 - 6x + 3 using the quadratic formula?

1 Answer
Alan P.
Apr 12, 2016

Single root at x=1 (multiplicity 2)

Explanation:

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

Given: y=3x^2-6x+3
color(white)("XXX")a=3
color(white)("XXX")b=-6
color(white)("XXX")c=3

So the roots are
color(white)("XXX")x=(6+-sqrt((-6)^2-4(3)(3)))/(2(3)

color(white)("XXXX")=(6+-sqrt(36-36))/6

color(white)("XXXX")=1

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