Quadratic Equation Calculator
Struggling with a quadratic equation? Our calculator instantly finds the roots, calculates the discriminant, tells you whether the roots are real or complex, and breaks down the parabola's key properties — perfect for students and quick problem-solving.
Quadratic Equation Calculator
Solve equations of the form ax² + bx + c = 0, find roots, discriminant, and vertex instantly.
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How the Quadratic Equation Calculator Works
Follow these simple steps to get accurate results instantly.
Enter Coefficients
Enter values for a, b, and c.
Calculate Discriminant
The calculator finds b² - 4ac.
Find Roots
Roots are calculated using the quadratic formula.
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
Verified answers to essential calculation and diagnostic questions.
A quadratic equation is a second-degree polynomial equation written as ax² + bx + c = 0.
The quadratic formula is x = (-b ± √(b² - 4ac)) / 2a.
The discriminant is b² - 4ac and determines the nature of the roots.
The equation has two distinct real roots.
The equation has one repeated real root.
The equation has two complex roots.
The x-coordinate of the vertex is given by x = -b / (2a). Substituting this x-value back into the quadratic function y = ax² + bx + c gives the corresponding y-coordinate.
Written & maintained by Aditya Singh
Aditya Singh is a software engineer and the founder of DevCalc, based in Uttar Pradesh, India. He builds and maintains every calculator on this site, using standard, verified formulas — the same ones used by banks, institutions, and educators — with careful attention to accuracy. Read more about the author →