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)

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