RootFinder

Polynomial Roots Calculator

Quadratic roots, real or complex.

Where the curve crosses zero

The roots of a polynomial are the x-values where it equals zero — graphically, where the curve crosses the x-axis. A quadratic can cross twice, touch once, or never cross at all (complex roots).

Why it matters beyond algebra class

Finding roots is how you solve for break-even points, the moment a projectile hits the ground, or any 'when does this equal zero' question in applied math.

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RootFinder

Polynomial Roots Calculator

Quadratic roots, real or complex.

a (x²)

b (x)

Roots

3, 2

Discriminant: 1

Solves quadratics. For higher-order polynomials, use numerical methods.

What you entered

a: 1b: -5c: 6

1
Discriminant
-5² − 4×1×6= 1
2
Two real roots
x = (−-5 ± √1) ÷ (2×1)= 3, 2

Result

Roots: 3, 2

For 1x² + -5x + 6 = 0, the discriminant is 1, giving roots 3, 2.

Where the curve crosses zero

The roots of a polynomial are the x-values where it equals zero — graphically, where the curve crosses the x-axis. A quadratic can cross twice, touch once, or never cross at all (complex roots).

Why it matters beyond algebra class

Finding roots is how you solve for break-even points, the moment a projectile hits the ground, or any 'when does this equal zero' question in applied math.