1. What is the Quadratic Formula?

The quadratic formula provides the solutions to a quadratic equation of the form ax² + bx + c = 0. It's a fundamental formula in algebra that works for all quadratic equations, including those with complex roots.

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) which determines the nature of the roots.

3. Types of Roots

Details: Depending on the discriminant value:

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

4. Using the Calculator

Tips: Enter the coefficients a, b, and c from your quadratic equation. The calculator will show all roots, whether real or complex.

5. Frequently Asked Questions (FAQ)

Q1: What if a is zero?
A: If a is zero, the equation is linear (not quadratic) and has exactly one root: x = -c/b.

Q2: Can the calculator handle complex roots?
A: Yes, it displays complex roots in the form a ± bi when the discriminant is negative.

Q3: How precise are the results?
A: Results are rounded to 4 decimal places for clarity.

Q4: What's the significance of the discriminant?
A: The discriminant (b² - 4ac) determines the nature and number of roots:

• Positive: Two real roots
• Zero: One real root
• Negative: Two complex roots

Q5: Can I use fractions or decimals?
A: Yes, the calculator accepts both decimal and fractional inputs (entered as decimals).