Math & science
Quadratic Equation Solver
Solve ax^2 + bx + c = 0 using the quadratic formula and view discriminant and vertex details.
Interactive calculator
Solve a quadratic equation
Enter coefficients for ax^2 + bx + c = 0 to calculate the discriminant, roots, and vertex information.
Results
Discriminant
1
Root 1
3
Root 2
2
Vertex
(2.5, -0.25)
Real-root form
How to use it
- 01Enter coefficients a, b, and c from the equation ax^2 + bx + c = 0.
- 02Review the discriminant to see whether the roots are real or complex.
- 03Use the roots and vertex information for graphing or solving follow-up questions.
Result guide
- Coefficient a must be non-zero or the equation is no longer quadratic.
- Positive discriminant gives two real roots, zero gives one repeated real root, and negative gives complex roots.
- Vertex coordinates help when graphing the parabola.
About this calculator
Quadratic-solver pages are useful in algebra classes, exam prep, and engineering contexts where users need roots quickly and accurately.
A stronger version should show more than just x values. The discriminant and vertex information help users understand the shape and behavior of the parabola too.
Frequently asked questions
What does the discriminant tell me?
It tells you whether the quadratic has two real roots, one repeated root, or complex roots.
Why is a not allowed to be zero?
Because if a equals zero, the x^2 term disappears and the equation becomes linear instead of quadratic.
Why show the vertex too?
Because it gives a quick view of the parabola's turning point, which is useful in graphing and optimization problems.
Method and limitations
This calculator uses the formula and assumptions described on this page. We do not claim independent professional review. Direct references will be listed here when they support a specific rule or data source used by this calculator.
Results are estimates for general information. Verify current rules and assumptions before making financial, tax, or health decisions.
Read our Editorial and Verification Policy →Related calculators
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