Quadratic Formula Calculator
Free online Quadratic Formula Calculator.
Calculator
How to Use
- Enter the required values
- Click Calculate to see the result
- Review the detailed output
Formula
For ax^2 + bx + c = 0: x = (-b +/- sqrt(b^2 - 4ac)) / (2a). Discriminant D = b^2 - 4ac determines root type: D>0 two real, D=0 one repeated, D<0 complex.
Example Calculations
Two Real Roots
Input: a=1, b=-5, c=6 (x^2 - 5x + 6 = 0)
Result: x = 3 and x = 2, Discriminant: 1
One Repeated Root
Input: a=1, b=-6, c=9 (x^2 - 6x + 9 = 0)
Result: x = 3 (repeated), Discriminant: 0
Complex Roots
Input: a=1, b=2, c=5 (x^2 + 2x + 5 = 0)
Result: x = -1 + 2i and x = -1 - 2i, Discriminant: -16
About This Calculator
Free online quadratic formula calculator. Calculate instantly in your browser with our easy-to-use tool. No sign-up required.
Our quadratic formula calculator is free, easy to use, and provides instant results. All calculations are performed in your browser for privacy and speed.
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Frequently Asked Questions
What is the quadratic formula?
x = (-b +/- sqrt(b^2 - 4ac)) / 2a, solving ax^2 + bx + c = 0.
What does the discriminant tell us?
b^2 - 4ac reveals root nature: positive = two real, zero = one repeated, negative = complex.
How to know if solutions are real?
If discriminant >= 0, solutions are real. If negative, they involve imaginary numbers.
Real-world applications?
Projectile motion, satellite dishes, bridge arches, profit maximization, and trajectories.
Solve without the formula?
Yes, by factoring, completing the square, or graphing. The formula always works.