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Quadratic Solver

Roots of ax² + bx + c = 0.

Free to use, no sign-up required. Quadratic Solver is one of 198 tools built into Xenition, alongside a chat that can use them for you.

Solves any quadratic equation ax² + bx + c = 0, giving real or complex roots, the discriminant, and a graph of the curve.

How to use Quadratic Solver

  1. Enter the coefficients a, b and c. a cannot be 0.
  2. Read the Roots.
  3. Check the Discriminant (Δ) and Root type.
  4. Look at the parabola for real roots, or the surface plot for complex ones.

How it works

The discriminant is Δ = b² − 4ac. If Δ > 0, the roots are (−b ± √Δ) ÷ 2a. If Δ = 0 there is one double root, −b ÷ 2a. If Δ < 0 the roots are complex: −b ÷ 2a ± (√−Δ ÷ 2a)i. Roots show up to four decimal places.

Example

For x² − 3x + 2 = 0, Δ = 9 − 8 = 1, so x = 2 and x = 1. For 2x² + x − 3 = 0, Δ = 25, giving x = 1 and x = −1.5. For x² + 2x + 5 = 0, Δ = −16, giving x = −1 ± 2i.

Questions about Quadratic Solver

What does a negative discriminant mean?

The parabola never crosses the x-axis, so there is no real number that solves the equation. The two solutions are complex numbers that are conjugates of each other.

Why must a not be zero?

With a = 0 the x² term disappears and the equation is linear, bx + c = 0, which has at most one solution, x = −c ÷ b.

Use it from chat

You do not have to open Quadratic Solver to use it. Ask Xenition in plain language and it runs the right tool, then carries the answer into whatever you are working on — a document, a spreadsheet, a deck.

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