Below is a quadratic formula calculator that solves quadratic equations in the form ax² + bx + c = 0. Enter your coefficients and the tool finds the roots (solutions).
Quadratic Formula Calculator
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Using the quadratic formula calculator
Enter the coefficients a, b, and c from your quadratic equation ax² + bx + c = 0. The calculator solves in real-time, displaying:
- Both roots (x₁ and x₂)
- The discriminant value and what it means
- Complex solutions when the discriminant is negative
- The vertex of the parabola
What is the quadratic formula?
The quadratic formula solves any quadratic equation of the form ax² + bx + c = 0:
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
The expression under the square root, b² - 4ac, is called the discriminant. It determines the nature of the solutions:
- Positive discriminant: Two distinct real solutions
- Zero discriminant: One repeated real solution
- Negative discriminant: Two complex (imaginary) solutions
Example calculation
For x² - 5x + 6 = 0 (a=1, b=-5, c=6):
\text{Discriminant} = (-5)^2 - 4(1)(6) = 25 - 24 = 1
x = \frac{5 \pm \sqrt{1}}{2} = \frac{5 \pm 1}{2}
Solutions: x = 3 and x = 2
