Math
Quadratic Formula Calculator
Use the quadratic formula calculator to solve quadratic equations and see whether the roots are real, repeated, or complex.
Roots
—
- Discriminant
- —
- Vertex x
- —
- Vertex y
- —
Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the quadratic formula calculator solves
Use the quadratic formula calculator to solve quadratic equations and see whether the roots are real, repeated, or complex.
Formula
How to use it
- Enter a, b, and c from ax^2 + bx + c = 0.
- Check the discriminant to classify the roots.
- Use the vertex values to understand the graph.
How to read the answer
Positive discriminants give two real roots, zero gives one repeated root, and negative discriminants give complex roots.
Common mistakes and edge cases
- a cannot be zero.
- Use the signs of b and c exactly as written.
- Remember the entire numerator is divided by 2a.
Worked examples
Two real roots
Roots
x = 2 or 1
Complex roots
Roots
x = -1 +/- 2i
Frequently asked questions
What is the discriminant?+
The discriminant is b^2 - 4ac. It tells how many roots the quadratic has and what kind they are.
Can the roots be decimals?+
Yes. Some quadratics factor cleanly, but the quadratic formula works even when roots are irrational or complex.
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Last updated: May 8, 2026