What is the description of a specific relationship under given conditions in the natural world known as ?

The discriminant () of a quadratic equation ax² + bx + c = 0 is written as b² - 4ac.

If Δ > 0, you will have two real roots.
If Δ = 0, you will have one real root.
If Δ < 0, you will have two complex roots.

Why? Let's take a look at the quadratic equation:



(Assuming a, b, and c are all real)
See the discriminant inside the square root?
If it's positive, we'll be left with a real number.
If it's negative, what's inside the root is imaginary, and so our solution is complex.
If it's equal to 0, we only get one solution. (plus/minus 0 has no effect)

If the discriminant of a quadratic equation is 4, B) There are two real roots.