How do Descriminants Work and why do they work this way

Question

I was taught in additional maths that the descriminant was b²-4ac and how this little equation affects how the quadratic curve interacts with a line
why do we need to take a this small segment from the quadratic equation and how does this equation interact with different lines.

In: Mathematics

Answer 1

The quadratic formula contains the discriminant formula inside a square root, with a +/- on the outside of it. If the discriminant is negative, the square root has no real values, so you can’t find a point where the quadratic crosses the x axis (since that’s what a solution to a quadratic means, a point where y=0). If it’s positive, you have 2 solutions, 1 for the + part of the +/- and 1 for the -. If it’s 0, then -0 is the same as +0 so there ends up only being 1 solution.