Quadratic Formula

Standard form, discriminant cases, and the ± quadratic formula for ax² + bx + c = 0.

Name	Formula	Note
Standard form	`ax² + bx + c = 0` a ≠ 0. Divide through if the leading coefficient is messy.	a ≠ 0. Divide through if the leading coefficient is messy.
Discriminant	`Δ = b² − 4ac` Sign of Δ tells how many real roots.	Sign of Δ tells how many real roots.
Two real roots	`Δ > 0` Two distinct real solutions.	Two distinct real solutions.
Repeated root	`Δ = 0` One real root (multiplicity two).	One real root (multiplicity two).
No real roots	`Δ < 0` Complex conjugate pair if you allow complex numbers.	Complex conjugate pair if you allow complex numbers.
Quadratic formula	`x = (−b ± √Δ) / (2a)` Both signs when Δ > 0.	Both signs when Δ > 0.

Open a calculator and put these formulas to work.