How do you find the discriminant?

The discriminant is calculated using the formula D = b² − 4ac. It determines how many real roots the equation has.

How many roots can a quadratic equation have?

If D > 0, there are two distinct real roots. If D = 0, there is one real root. If D < 0, there are no real roots.

What is the quadratic formula?

The roots are found using x = (-b ± √D) / (2a).

What happens if a = 0?

If a = 0, the equation is not quadratic anymore. In that case, a linear equation solver should be used.

Does this calculator show step-by-step results?

Yes, the calculator shows coefficient substitution, discriminant calculation, and the root formulas.

Quadratic Equation Calculator

Solve equations of the form ax² + bx + c = 0, calculate the discriminant, find the roots, and see a step-by-step explanation.

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a·x² + b·x + c = 0

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Quadratic Equation Calculator — How It Works

This calculator helps you solve quadratic equations in the form ax² + bx + c = 0. It automatically calculates the discriminant, determines the number of roots, and shows a step-by-step solution.

Quadratic Equation Form

The standard form is: ax² + bx + c = 0, where a ≠ 0.

Discriminant

To find the roots, first calculate the discriminant:

D = b² − 4ac

The value of the discriminant determines the number of real solutions.

D > 0 — two distinct real roots
D = 0 — one real root
D < 0 — no real roots

Quadratic Formula

If D ≥ 0, the roots are found using:

x₁ = (-b + √D) / (2a)
x₂ = (-b − √D) / (2a)

Example

For the equation x² − 3x + 2 = 0:

a = 1, b = -3, c = 2
D = (-3)² − 4·1·2 = 9 − 8 = 1
x₁ = 2, x₂ = 1

When not to use this calculator

If a = 0, the equation is no longer quadratic. In that case, you should use a linear equation solver.

Frequently Asked Questions

What is a quadratic equation?

It is an equation in the form ax² + bx + c = 0, where a ≠ 0.

What does the discriminant show?

The discriminant shows how many real roots the equation has: two, one, or none.

What if D is less than zero?

Then the equation has no real roots. If needed, it can be solved in complex numbers.

Why can’t a be zero?

Because then the ax² term disappears and the equation becomes linear, not quadratic.

Does the calculator show steps?

Yes, it shows substitution into the discriminant formula and the root formulas.

Can I enter decimal numbers?

Yes, both integers and decimal coefficients are supported.