1. What is the Quadratic Formula?

The quadratic formula provides the solutions to quadratic equations of the form ax² + bx + c = 0. It's one of the most fundamental formulas in algebra and is used to find the roots (solutions) of quadratic equations.

2. How Does the Calculator Work?

The calculator uses the quadratic formula:

Where:

• \( a \) — Coefficient of x² (must not be zero)
• \( b \) — Coefficient of x
• \( c \) — Constant term

Explanation: The formula calculates the roots by considering the discriminant (b² - 4ac). The discriminant determines the nature of the roots:

• Positive discriminant: Two distinct real roots
• Zero discriminant: One real root (repeated)
• Negative discriminant: Two complex conjugate roots

3. Importance of Quadratic Equations

Details: Quadratic equations appear in various fields including physics, engineering, economics, and optimization problems. They describe parabolic relationships and are fundamental in mathematical modeling.

4. Using the Calculator

Tips: Enter the coefficients a, b, and c from your quadratic equation ax² + bx + c = 0. The coefficient 'a' must be non-zero for it to be a quadratic equation.

5. Frequently Asked Questions (FAQ)

Q1: What if I get complex number results?
A: Complex roots indicate the parabola doesn't intersect the x-axis. The solutions are valid mathematically but don't correspond to real x-intercepts.

Q2: Why can't 'a' be zero?
A: If a=0, the equation becomes linear (bx + c = 0), not quadratic. The formula would involve division by zero.

Q3: What's the geometric interpretation?
A: The roots represent the x-intercepts of the parabola y = ax² + bx + c. Complex roots mean no real x-intercepts.

Q4: How accurate are the results?
A: The calculator provides solutions rounded to 4 decimal places. For exact fractions, symbolic computation would be needed.

Q5: Can this solve higher-degree equations?
A: No, this is specifically for quadratic (degree 2) equations. Cubic and quartic equations have more complex formulas.