Quadratic Formula Calculator
Solve quadratic equations of the form ax² + bx + c = 0 using the quadratic formula. Get step-by-step solutions with real and complex roots.
Enter Coefficients
Cannot be zero
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Solution
Equation
Discriminant Analysis
Solutions
Additional Information
Step-by-step Solution
Frequently Asked Questions
The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to solve quadratic equations of the form ax² + bx + c = 0 where a ≠ 0.
The discriminant (b² - 4ac) determines the nature of roots: positive means two real roots, zero means one repeated root, negative means two complex roots.
Yes, when the discriminant is negative, the calculator will display complex roots in the form a + bi.
If a = 0, the equation becomes linear (bx + c = 0) rather than quadratic. The calculator will alert you to this.
Results are calculated with high precision and displayed according to your selected decimal places (2-8 digits).
Yes, enable "Show detailed steps" to see the complete solution process including discriminant calculation and formula application.
Quadratic equations appear in physics (projectile motion), business (profit optimization), engineering (parabolic structures), and many other fields.
The vertex represents the maximum or minimum point of the parabola, while the axis of symmetry is the vertical line x = -b/(2a) that divides the parabola into two equal halves.
Disclaimer
This calculator is provided for educational purposes only. While we strive for accuracy, please verify important calculations independently. The results should not be used for critical applications without proper verification.