x = (−b ± √(b²−4ac)) ÷ 2a. The discriminant (b²−4ac) determines the nature of roots: positive = 2 real roots, zero = 1 real root, negative = complex roots.
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Frequently Asked Questions
What is the discriminant?+
The discriminant is b²−4ac. If positive: two distinct real roots. If zero: one repeated root. If negative: two complex (imaginary) roots.
What is a quadratic equation used for?+
Quadratics model projectile motion, profit maximisation, area problems and many engineering applications.
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