How to use the discriminant to find out what type of solutions the equation has for #-x^2 + 4x – 4 = 0#?
The discriminant is used to determine whether there are any solutions at all. It is really just part of the quadratic formula.
So we have:
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
Notice how if you divide the middle term by 2 and square it, you ger 4, so this is a perfect square. This is:
Or, as it was written: