Quadratic Equation Solver — Exact Radical Roots & Vertex

How to use

1. Type coefficients a, b and c (decimals allowed).
2. Press Solve.
3. Read the exact radical roots, decimals, discriminant, vertex and axis.
4. Copy the factored form when the roots come out rational.

About this tool

Type a, b and c — the tool takes it from there. If a is zero it quietly becomes a linear solver; otherwise it computes the discriminant b²−4ac exactly, then reports the roots in three useful forms: the exact radical (with square factors pulled out of the radicand and the whole expression reduced, like (−3 ± √5)/2), the decimal values, and — when the roots are rational — the factored form a(x−r₁)(x−r₂). You also get the vertex, the axis of symmetry and a plain-English presentation for complex roots such as (−1 ± √3·i)/2. Decimal coefficients are converted to exact fractions internally, so 'exact' means exact. A genuinely useful check for algebra homework, running entirely in your browser.

FAQ

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