Calculator for Quadratic Equation

Formula

x = [−b ± √(b² − 4ac)] ÷ 2a. Di discriminant D = b² − 4ac dey decide di root type: D > 0 dey give two different real roots, D = 0 dey give one repeated root, D < 0 dey give two complex roots. Di vertex x-coordinate na x = −b ÷ 2a.

Example wey show the calculation

x² − 5x + 6 = 0: a = 1, b = −5, c = 6. Discriminant = (−5)² − 4 × 1 × 6 = 25 − 24 = 1. Roots = [5 ± √1] ÷ 2, so x = 3 and x = 2. Check: 3² − 15 + 6 = 0 and 2² − 10 + 6 = 0. The vertex dey at x = 2.5.

Where e fit work and limits

If a no be zero, di equation na quadratic. If a na zero, di page go show di linear or constant-equation case. Results normally show 12 significant digits; dem fit increase to 17 to separate roots wey close. Very small or large values dey use scientific notation. Di precision of decimal input still dey limit accuracy, especially near repeated roots. If di number size pass wetin di tool support, e go show error instead of infinity or false zero.

W. Kahan (2004), Qdrtcs

Version of di formula: fd252bec1aa3 · Example don get check: 2026-10-31

Questions wey people dey ask often

What if a na zero?

Then solve bx + c = 0. If b no be zero, x = −c ÷ b. If b and c both na zero, every real x go work; if b na zero but c no be zero, no solution dey.

Wetin the discriminant dey tell me?

Whether roots na real numbers and how many dem be: positive mean two different real roots; zero mean one repeated root; negative mean no real roots — the parabola no cross the x-axis.

Wetin be complex roots?

When discriminant negative, the roots involve i (square root of −1). For x² + 2x + 5 = 0, the roots na −1 + 2i and −1 − 2i. Dem na correct solutions for complex numbers; dem just no be points on the real x-axis.

Why two roots dey?

Polynomial of degree 2 get two roots if you count repeated roots. Di roots fit be di same or form complex pair, but if you count multiplicity, na two roots always dey.

I suppose use factorization instead?

Factoring dey faster when roots na small integers, like the example (x − 3)(x − 2). The formula dey work even when factoring no obvious.

The vertex matter?

Na di vertex of di parabola: minimum when a > 0, maximum when a < 0. Im x-coordinate dey exactly halfway between di two real roots when dem dey.

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