CalmCalc
MATH

Quadratic Formula Calculator

Calculate first root using a, b, c

FIRST ROOT3

Real roots from the quadratic formula.

First root
3
Second root
2
Discriminant
1
Vertex
(2.5, -0.25)
Estimate based on the values shown
MethodReports real roots or a complex-conjugate pair, plus discriminant and vertex.

Before you use the result

The result depends on the entered values, selected mode, and displayed mathematical assumptions.

EDITORIAL NOTES

Using the Quadratic Formula Calculator responsibly

Page-specific guidance based on this calculator’s implemented method, inputs, and known limits.

What this result is useful for

The quadratic formula solves equations of the form ax² + bx + c = 0 and reports the nature of the roots from the discriminant. It is useful when factoring is inconvenient or when exact and approximate roots need to be compared.

Assumptions and limits

The leading coefficient must not be zero; otherwise the equation is linear. A negative discriminant produces complex roots. Displayed decimal roots may be rounded even when an exact radical form exists.

How to check the result

Substitute each reported root into the original polynomial and confirm that the result is zero within rounding tolerance. The sum of the roots should equal −b/a and their product should equal c/a.

Content review: August 21, 2026
INTERPRET THE RESULTRead the math guideCheck assumptions, limitations and comparison methods →