Quadratic Equation Calculator
Solution:
 |
| Quadratic Equation Solver Online Tool |
Quadratic Equation Solver - Solve ax² + bx + c = 0 Equations
Our free online Quadratic Formula Calculator helps you solve any quadratic equation instantly. Simply enter the coefficients a, b, and c of your equation in the form ax² + bx + c = 0, and our solver will calculate the roots and discriminant with step-by-step explanations.
Our free online Quadratic Formula Calculator helps you solve any quadratic equation instantly. Simply enter the coefficients a, b, and c of your equation in the form ax² + bx + c = 0, and our solver will calculate the roots and discriminant with step-by-step explanations.
What is a Quadratic Equation?
A quadratic equation is a second-degree polynomial equation in a single variable x, with a ≠ 0, expressed in the form ax² + bx + c = 0. The solutions to quadratic equations are called roots, and they represent the x-values where the parabola crosses the x-axis.
The Quadratic Formula
The quadratic formula is the universal method for solving all quadratic equations:
x = [-b ± √(b² - 4ac)] / (2a)
Understanding the Discriminant
The expression under the square root in the quadratic formula (b² - 4ac) is called the discriminant. It determines the nature of the roots:
- Positive Discriminant: Two distinct real roots
- Zero Discriminant: One real root (repeated solution)
- Negative Discriminant: Two complex roots
Step-by-Step Solving Process
Our quadratic equation solver follows these steps:
- Identify the coefficients a, b, and c from your equation
- Calculate the discriminant (D = b² - 4ac)
- Determine the nature of roots based on the discriminant
- Apply the quadratic formula to find the exact solutions
- Simplify the results to their simplest form
Real-World Applications of Quadratic Equations
Quadratic equations have numerous practical applications in physics, engineering, economics, and computer graphics. They are used to model projectile motion, optimize profit calculations, design parabolic mirrors and satellite dishes, and much more.
Frequently Asked Questions
Can this solver handle fractional coefficients?
Yes, our quadratic equation calculator accepts both integer and fractional coefficients. Simply enter the fractions as decimals or use the appropriate format.
What if the equation has no real solutions?
If the discriminant is negative, the equation has no real solutions but two complex solutions. Our calculator will display both complex roots in the form a ± bi.
Does the calculator show the solving steps?
Yes, our quadratic formula calculator provides step-by-step explanations showing how it arrived at the solution, including the discriminant calculation and application of the quadratic formula.
Can I solve quadratic equations with complex coefficients?
This version of the calculator is designed for real coefficients. For equations with complex coefficients, you might need specialized mathematical software.
Is this quadratic equation solver free to use?
Yes, our calculator is completely free to use with no limitations or registration requirements.
