Question about the usage of the (part of) the quadratic formula

Question

Hi guys, I just remembered a lot of people using sqrt(b\^2-4ac)/(2a) to solve a common math problem. I can't seem to remember what it's used for and I would really appreciate if someone could refresh my memory because I think it might be important to use! Sorry for my informality and lack of detail, I'm trying my hardest to remember everything. I might be wrong, but is this used to determine how many possible solutions there can be for that quadratic? Thanks and sorry in advance!

Answer 1

This is called the determinant of a quadratic equation and is used to determine the number of real solutions. if it is *+ there are 2 real solutions

if it is zero there is only 1 solution

if it is - there are no real solutions as the square root of a negative number is imaginary