Math

Cubic Equation Calculator

Find a real root of ax³ + bx² + cx + d = 0.

Calculated Output

A real root 1

Formula: Solved numerically (Newton's method) for a real root

Step-by-Step Breakdown

1. Values used:

2. a = 1

3. b = -6

4. c = 11

5. d = -6

7. A real root = 1

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The math behind it

A cubic always has at least one real root. Newton's method iterates xₙ₊₁ = xₙ − f(xₙ)/f′(xₙ) until it converges.

x³ − 6x² + 11x − 6 = 0 has roots 1, 2 and 3; the tool returns one of them.

Does it find all three roots?

It returns one real root. Divide it out to reduce the cubic to a quadratic for the remaining roots.