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Open toolQuadratic Equation Solver
Solve a quadratic equation from coefficients a, b, and c. Review the discriminant and the rounded real or complex roots.
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How Quadratic Equation Solver works
The discriminant determines which form of the quadratic root calculation applies.
The solver calculates b squared minus four times a times c. A nonnegative discriminant is used in the quadratic formula for real roots; a negative one is represented as a real part plus or minus an imaginary component.
Coefficient a must be nonzero. Results are rounded for display; exact algebraic forms are not generated.
How to use Quadratic Equation Solver
Enter coefficients for a quadratic written with all terms on one side of the equation.
Enter the three equation coefficients
Enter a, b, and c from a quadratic written in the form ax squared plus bx plus c equals zero. Keep coefficient signs intact. The a coefficient must be nonzero, because this form does not switch to solving a linear equation.
Coefficient a
Calculate the discriminant and roots
Select Calculate and read the root result and its type. The discriminant decides whether the answer has two real roots, one repeated real root, or complex conjugates. Check the entered signs if the expected type differs from the result.
0 ± 1i
Review the rounded components
Read the discriminant and supporting roots or real and imaginary components. Values are rounded to four decimal places for display; exact radical forms are not generated. Keep the original coefficients when checking a rounded root in another calculation.
Discriminant
Quadratic formula examples with real and complex roots
Use explicit coefficient examples so the equation being solved remains clear.
Check two real roots of a factorable quadratic
The hypothetical equation x squared minus five x plus six equals zero has roots two and three. Enter a as one, b as negative five and c as six. This is a direct check of coefficient signs and the two root result.
Inspect a repeated root
Use coefficients that produce a zero discriminant to see the repeated real root case. The result label distinguishes it from two distinct roots. A numerical display alone can make equal roots look like an omitted answer unless that label is retained.
Review a complex root result
For a negative discriminant, read the real part and imaginary magnitude together with the conjugate pair. The output uses rounded numerical values. It does not generate exact symbolic expressions or explain a full algebraic derivation for the entered equation.
Use rounded roots with the original equation
Read the root type and rounding with the original coefficients.
Real roots are displayed to four decimal places. Substituting a rounded root into the original equation can leave a small residual, so the display should not be treated as an exact symbolic expression.
The discriminant determines the root type in the entered numerical model. Complex roots are given as a conjugate pair. Exact radicals, symbolic simplification and graph plotting are not part of this tool's output.
Check signs and missing terms
Check coefficient signs and the nonzero quadratic term before solving.
A zero a coefficient is rejected because the equation would no longer be quadratic. Use the equation's correct form rather than entering an arbitrary nonzero value to get a result. Preserve minus signs when moving terms.
If the answer differs from a worked example, compare every coefficient and its sign first. The calculator does not parse variables or an equation string. Keep numerical precision in mind when checking a displayed root by substitution.
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Open toolUse Quadratic Equation Solver
Solve a quadratic equation from coefficients a, b, and c.
Quadratic Equation Solver: common questions
Answers about using Quadratic Equation Solver and understanding its results.
What if the discriminant is zero?
The equation has one repeated real root.
Can it show complex roots?
Yes. A negative discriminant is displayed as a real part plus or minus an imaginary part.
Can a be zero?
No. A zero a coefficient makes the equation non-quadratic. This form asks for a nonzero a rather than switching to a linear solver.
Does it return exact radicals?
No. Roots are formatted to four decimal places. Check rounding before using the displayed values in further calculations.