How to use the discriminant to find out what type of solutions the equation has for #-x^2 + 4x – 4 = 0#?

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Answer 1 · 2015-05-25T19:06:34

The discriminant is used to determine whether there are any solutions at all. It is really just part of the quadratic formula.

#sqrt(b^2 - 4ac)#

With #(-)x^2 + (4)x + (-4) = 0#:
#a = -1#
#b = 4#
#c = -4#

So we have:
#sqrt(4^2 - 4(-1)(-4)) = sqrt(16-16) = 0#
meaning that this equation has solutions. The solutions can be determined by factoring.

If you divide by -1, you can make this look nicer, and #0/(-1) = 0#:
#x^2 - 4x + 4 = 0#

Notice how if you divide the middle term by 2 and square it, you ger 4, so this is a perfect square. This is:

#(x-2)(x-2) = (x-2)^2 = 0#

Or, as it was written:
#-(x-2)(x-2) = -(x-2)^2 = 0#

#x = 2# (multiplicity 2)