About This Quadratic Equation Calculator

This calculator solves quadratic equations written as ax² + bx + c = 0. It uses the quadratic formula to find the roots of the equation and shows the discriminant, root type, and calculation steps.

It is useful for algebra homework, exam practice, graph analysis, and checking manual calculations. The tool supports equations with two real roots, one repeated root, and complex roots.

Quadratic Formula

The quadratic formula is:

In this formula, a, b, and c are the coefficients of the quadratic equation. The expression b² - 4ac is called the discriminant.

What the Discriminant Means

• D > 0: the equation has two different real roots.
• D = 0: the equation has one repeated real root.
• D < 0: the equation has two complex roots.

How to Use the Calculator

• Enter the value of a, b, and c.
• Make sure a is not zero for a true quadratic equation.
• Choose the number of decimal places you want.
• Click Calculate Roots to see the answer and steps.

Common Quadratic Equation Examples

Example 1: Two real roots

For x² - 5x + 6 = 0, the roots are x = 2 and x = 3.

Example 2: One repeated root

For x² + 2x + 1 = 0, the repeated root is x = -1.

Example 3: Complex roots

For x² + x + 1 = 0, the discriminant is negative, so the roots are complex numbers.

FAQ

What is a quadratic equation?

A quadratic equation is a second-degree equation that can be written as ax² + bx + c = 0, where a is not equal to zero.

Can a quadratic equation have no real solution?

Yes. If the discriminant is negative, the equation has no real roots. Instead, it has two complex roots.

Why can’t a be zero?

If a is zero, the x² term disappears and the equation becomes linear instead of quadratic.

Is this calculator suitable for school use?

Yes. It shows both the final answer and the main calculation steps, making it helpful for learning and checking algebra work.