Quadratic Equation Calculator
Solve quadratic equations instantly using our free Quadratic Equation Calculator. Find roots, discriminant, vertex, and nature of roots for equations in the form ax² + bx + c = 0.
Use our free online quadratic equation calculator to get accurate results instantly. The calculator is designed to be fast, easy to use, mobile-friendly, and suitable for everyday calculations.
Quadratic Equation Calculator
Solve equations of the form ax² + bx + c = 0, find roots, discriminant, and vertex instantly.
How the Quadratic Equation Calculator Works
Step 1
Enter Coefficients
Enter values for a, b, and c.
Step 2
Calculate Discriminant
The calculator finds b² - 4ac.
Step 3
Find Roots
Roots are calculated using the quadratic formula.
Step 4
View Results
See roots, discriminant, and root type.
Quadratic Formula
x = (-b ± √(b² - 4ac)) / 2a
A quadratic equation is written as ax² + bx + c = 0. The quadratic formula calculates the roots of the equation using the coefficients a, b, and c.
Example Calculation
Input: a=1, b=-5, c=6
Output: Roots = 2 and 3
Common Uses
- • Algebra
- • Mathematics Education
- • Engineering
- • Physics
- • Competitive Exams
- • Graph Analysis
- • Research
- • Polynomial Equations
Frequently Asked Questions
What is a quadratic equation?
A quadratic equation is a second-degree polynomial equation written as ax² + bx + c = 0.
What is the quadratic formula?
The quadratic formula is x = (-b ± √(b² - 4ac)) / 2a.
What is the discriminant?
The discriminant is b² - 4ac and determines the nature of the roots.
What happens if the discriminant is positive?
The equation has two distinct real roots.
What happens if the discriminant is zero?
The equation has one repeated real root.
What happens if the discriminant is negative?
The equation has two complex roots.
Is this calculator free?
Yes, the Quadratic Equation Calculator is completely free to use.
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