What is the Quadratic Equation Calculator?
The quadratic equation calculator solves equations of the form ax² + bx + c = 0 using the quadratic formula. It returns real roots, a repeated root or a complex pair.
How to use the Quadratic Equation tool
- Enter a (x² coefficient), b (x coefficient) and c (constant).
- The result updates instantly as you type, or press Calculate.
- Use Try an example to see how it works, and Reset to start again.
Formula
x = (−b ± √(b² − 4ac)) ÷ 2a. The discriminant b² − 4ac decides the number of real roots.
Worked example
With a (x² coefficient) 1, b (x coefficient) -3, c (constant) -10, the root x1 comes to 5. Root x2: -2; Discriminant: 49.
Frequently asked questions
What does the discriminant tell me?
Positive means two real roots, zero means one repeated root, negative means two complex roots.
What if a is zero?
Then it is not quadratic. It becomes a linear equation bx + c = 0.
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Checked by Calcovate · Formula tested against worked examples · Updated 7 Nov 2026 · How we check our calculators.