Last updated: November 19, 2025
Quadratic formula calculator explained
Quadratic equations of the form have up to two solutions. This calculator applies the quadratic formula, reports the discriminant to show how many real roots exist, and works with any coefficients.
How the conversion works
Given coefficients , , and (with ):
The discriminant determines the nature of the roots (positive = two real roots, zero = one repeated root, negative = complex roots). The calculator also handles negative values and displays complex results when needed.
Units and conversions
Coefficients are unitless unless you assign context (physics problems, finance, etc.). Enter integers or decimals; the roots inherit the same numeric scale.
Worked examples
- Two real roots
(, , ).
Roots: → , .
- Complex roots
(, , ).
Roots: .
Tips and pitfalls
- Ensure ; otherwise the equation is linear.
- Factor first when coefficients are small; factoring often reveals integer roots faster.
- When is negative, expect complex conjugate roots; the calculator displays them with notation.
- For numerical stability in floating-point contexts, use the reformulated quadratic formula to avoid subtractive cancellation (outside the scope of this simple tool).