1. What is the Quadratic Formula?

The quadratic formula provides the solutions to equations of the form ax² + bx + c = 0. It's derived by completing the square of the general quadratic equation.

2. How Does the Calculator Work?

The calculator uses the quadratic formula:

Where:

• \( a \) — Coefficient of x² (cannot be zero)
• \( b \) — Coefficient of x
• \( c \) — Constant term
• \( \sqrt{b^2 - 4ac} \) — Discriminant (determines nature of roots)

Explanation: The formula calculates the x-intercepts (roots) of the quadratic function by considering all possible cases of the discriminant.

3. Understanding the Solutions

Three cases:

1. Positive discriminant: Two distinct real roots
2. Zero discriminant: One real root (repeated)
3. Negative discriminant: Two complex conjugate roots

4. Using the Calculator

Tips: Enter coefficients a, b, and c of your quadratic equation (ax² + bx + c = 0). The calculator handles all cases including complex roots.

5. Frequently Asked Questions (FAQ)

Q1: What if a = 0?
A: The equation becomes linear (bx + c = 0). This calculator only solves quadratic equations where a ≠ 0.

Q2: Why do I get complex numbers?
A: When the discriminant is negative, the solutions are complex conjugates, meaning the parabola doesn't cross the x-axis.

Q3: How accurate are the results?
A: Results are rounded to 4 decimal places. For exact solutions, use symbolic computation.

Q4: Can this solve higher-degree equations?
A: No, this only solves quadratic equations. Cubic and quartic equations require more complex formulas.

Q5: What's the geometric interpretation?
A: The solutions represent the x-intercepts of the parabola described by y = ax² + bx + c.