The Discriminant
One number tells you how many real roots a quadratic has.
Concept
Under the radical
The quadratic formula puts b² − 4ac under a square root. That expression is the discriminant, written Δ.
Δ > 0: two real roots. Δ = 0: one repeated root. Δ < 0: no real roots (two complex ones).
Δ = b² − 4ac