MATH

Quadratic Formula Calculator

Estimate first root from a, b, c with the Quadratic Formula Calculator.

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.

CALCULATOR GUIDE

How to use the Quadratic Formula Calculator

Estimate first root from a, b, c with the Quadratic Formula Calculator. Use it to check the arithmetic while keeping the displayed method and entered values with your work.

Step by step

For the Quadratic Formula example, enter a, b, c. Keep each value in the unit displayed beside its field.
Review the selected Quadratic Formula workflow and inputs, then read first root in the result panel.
Change one Quadratic Formula assumption at a time to compare scenarios. Use Reset to restore this tool's worked example values.

How the calculation works

Reports real roots or a complex-conjugate pair, plus discriminant and vertex.

Worked example

To reproduce the Quadratic Formula worked example, reset the calculator. Use a 1; b -5; c 6. The result is first root of 3. Real roots from the quadratic formula. Review the displayed units before comparing the result.

Understanding the result

The Quadratic Formula reports first root. Use it to check the arithmetic while keeping the displayed method and entered values with your work. The result depends on the entered values, selected mode, and displayed mathematical assumptions.

How to check the answer

Check the Quadratic Formula answer by substituting first root back into the stated relationship. Test a simple value such as zero, one, or an equal pair, then confirm that sign, scale, units, and rounding match Reports real roots or a complex-conjugate pair, plus discriminant and vertex.

Common questions

What does the Quadratic Formula calculate?

Estimate first root from a, b, c with the Quadratic Formula Calculator.

Which inputs does the Quadratic Formula example use?

The worked example uses a, b, c. Other workflows can show different fields. Keep the chosen workflow and units with the result when comparing calculations.

Is the Quadratic Formula result exact?

The result depends on the entered values, selected mode, and displayed mathematical assumptions. Recheck a, b, c and use first root only for a decision where that level of precision is appropriate.

INTERPRET THE RESULTRead the math guideCheck assumptions, limitations and comparison methods →

KEEP GOING

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