Quadratic Equation Calculator
Solve quadratic equations and find the roots.
Quadratic Formula:
x = (−b ± √(b² − 4ac)) ÷ 2a
- • Discriminant > 0: two real roots
- • Discriminant = 0: one repeated root
- • Discriminant < 0: complex roots
What is Quadratic Equation Calculator?
A quadratic equation calculator solves equations of the form ax² + bx + c = 0 and shows the roots, discriminant, and vertex.
Quadratic equations model projectile motion, profit curves, and many real-world relationships.
How does the Quadratic Equation Calculator work?
The discriminant (b² – 4ac) determines the nature of the roots: two real, one repeated, or two complex.
The calculator shows both roots and the vertex of the parabola.
How to use the Quadratic Equation Calculator?
- Enter the coefficients a, b, and c.
- The calculator shows the roots, discriminant, and vertex.
Example
Try the calculator with your own numbers
- Enter your values in the input fields above.
- Adjust the values to match your situation.
- The result updates instantly as you change the inputs.
Benefits of using the Quadratic Equation Calculator
- Solve quadratic problems instantly.
- Understand root types via the discriminant.
- Check homework and exam answers.
Who should use the Quadratic Equation Calculator?
- Students practising problems and verifying homework answers.
- Teachers preparing examples and checking student work.
- Engineers and analysts who need quick, reliable calculations.
- Anyone who wants to double-check manual arithmetic.
Tips for getting the most out of the Quadratic Equation Calculator
- Check your inputs for typos — a single wrong digit changes the result completely.
- Use the result to verify your manual working, not to replace understanding.
- Try a simple case first (like 0 or 1) to make sure the output makes sense.
Frequently Asked Questions
What does the discriminant tell us?
If b² – 4ac > 0 there are two real roots; if = 0 one repeated root; if < 0 two complex roots.
What is the vertex?
The vertex is the parabola's highest or lowest point, at x = –b/2a.
The Quadratic Equation Calculator turns a tedious calculation into an instant answer, so you can focus on understanding the concept instead of the arithmetic.
Related Calculators
Quadratic Equation Calculator
Solve a quadratic equation ax² + bx + c = 0 and find its roots.
Polynomial Equation Solver Calculator
Solve a quadratic polynomial equation ax² + bx + c = 0.
2nd Degree Equation Calculator
Solve a second degree equation ax² + bx + c = 0.
Cubic Equation Solver Calculator
Solve a cubic equation ax³ + bx² + cx + d = 0 (find one real root).
Differential Equation Calculator
Solve a simple differential equation dy/dx = ax.
Equation Calculator
Solve a linear equation ax + b = c for x.