Quadratic Equation Calculator
Solve quadratic equations in the form ax² + bx + c = 0 and get the roots, discriminant, and complete step-by-step calculation.
Solve a quadratic equation
Enter the coefficients of your quadratic equation. The calculator will find the roots and show how the answer was calculated.
Your result
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| Equation | — |
| Coefficient a | — |
| Coefficient b | — |
| Constant c | — |
| Discriminant | — |
| Number of real roots | — |
Step-by-step calculation
What is a quadratic equation?
A quadratic equation is a second-degree polynomial equation that can be written in the standard form ax² + bx + c = 0, where a, b, and c are constants and a is not zero.
The values of x that make the equation equal to zero are called its roots or solutions.
How is a quadratic equation solved?
The quadratic formula can be used to solve any quadratic equation. First, the discriminant is calculated using b² − 4ac.
The value of the discriminant determines the number and type of real solutions. A positive discriminant gives two distinct real roots, zero gives one repeated real root, and a negative discriminant gives two complex roots.
Quadratic equation example
Consider the equation:
Here:
a = 1
b = −5
c = 6
Discriminant = (−5)² − 4(1)(6)
= 25 − 24
= 1
x = (5 ± √1) ÷ 2
x₁ = 3
x₂ = 2
Therefore, the solutions are x = 3 and x = 2.
Formula used
ax² + bx + c = 0
Discriminant:
Δ = b² − 4ac
Quadratic formula:
x = (−b ± √(b² − 4ac)) ÷ 2a
The discriminant is used to determine whether the equation has two real roots, one repeated real root, or two complex roots.
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Important: This calculator is provided for general informational and educational purposes only. The results are based on the coefficients entered and standard mathematical formulas. Always verify important calculations independently when accuracy is critical.