Loading…
Solve ax² + bx + c = 0, including complex conjugate roots.
Quadratic Equation Solver is loading — interactive editor will appear here. Use examples below to try instantly once loaded.
Press ? for keyboard shortcuts
Solves quadratic equations ax² + bx + c = 0 for real and complex roots, using the numerically stable form of the quadratic formula.
Quadratics show up in algebra class, physics (kinematics), and optimization. The naive −b ± √(b²−4ac) loses precision when |b| is much larger than the discriminant; the stable form avoids that, and complex roots are reported properly instead of as an error.
This tool is part of the DevStackIO platform — a collection of free online developer tools from DevStackIO. Browse more free developer resources on DevStackIO.
Algebra and pre-calculus students, teachers writing answer keys, and engineers working through kinematics or optimization by hand.
Enter coefficients a, b, and c
a cannot be zero — that's a linear equation, not a quadratic
Read the discriminant and roots (real or complex) in the result panel
1, −3, 2 → roots 1 and 22, −4, −2 → roots 1 ± √2 (≈ −0.414, 2.414)1, 0, 1 → complex: ±i (0 + 1i, 0 − 1i)1, −2, 1 → repeated root x = 1 (Δ = 0)Q: What does the discriminant tell me?
A: Its sign classifies roots: positive → two distinct reals, zero → one repeated, negative → complex conjugates.
Q: Why the 'numerically stable' form? A: When |b| >> √(4ac), one of the two naive roots subtracts nearly-equal numbers and loses precision
the q-form avoids it.
Q: Are complex roots shown exactly?
A: As a ± bi with decimal precision; exact radicals aren't expanded.
Q: Can this handle fractional coefficients? A: Yes
coefficients are plain real numbers.
Authoritative specifications, standards, and in-depth reading for Quadratic Equation Solver.
Discriminant Δ = 1 — two real roots
x1 = 2
x2 = 1
Quadratic formula with the numerically stable root form to avoid catastrophic cancellation. Complex roots shown as a ± bi. Runs locally.
Add, subtract, multiply, and divide fractions with exact rational arithmetic — no floating-point drift. Simplifies automatically.
Scientific calculator with trig and logs. Use for advanced math; for datasets use statistics-calculator. Input: expression. Returns result. 100% client-side, files never leave browser.
Simplify ratios, split a total in a given ratio, and solve proportions a:b = c:x.
Greatest common divisor and least common multiple of two or more numbers via Euclid's algorithm.
Descriptive statistics for a list of numbers: mean, median, mode, range, variance, standard deviation.
Compute nCr (combinations) and nPr (permutations) with exact integer arithmetic. Supports large n via logarithms.
Splits restaurant bills from subtotal, tip %, tax and party size. Use when dining out or splitting; differs from vat-gst by gratuity split vs tax-inclusive pricing. Returns tip amount, total and per-person share. 100% client-side.
Compute mean, median and stddev. Use for datasets; for single expressions use scientific-calculator. Input: numbers ≤10MB. Returns stats. 100% client-side, files never leave browser.