Quadratic Formula and the Discriminant

Quadratic Formula

For ax² + bx + c = 0,

x = [-b ± √(b² - 4ac)] / 2a

This works for all quadratics.

Example

2x² + 5x - 3 = 0
a=2, b=5, c=-3
x = [-5 ± √(25 - 4×2×-3)] / 4 = [-5 ± √49] / 4 = [-5 ± 7] / 4
x = 1/2 or x = -3

Discriminant: Δ = b² - 4ac

Δ > 0: Two distinct real roots

Δ = 0: One repeated real root

Δ < 0: No real roots

Discussion

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