1. What is the Quadratic Formula?

The quadratic formula provides the solutions to quadratic equations of the form ax² + bx + c = 0. It's a fundamental tool in algebra that works for all quadratic equations with real or complex coefficients.

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
• \( \pm \) — Indicates two possible solutions

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

3. Types of Roots

Details: The discriminant (D = b² - 4ac) determines the nature of the roots:

• D > 0: Two distinct real roots
• D = 0: Exactly one real root (a repeated root)
• D < 0: Two complex conjugate roots

4. Using the Calculator

Tips: Enter coefficients a, b, and c. The coefficient 'a' must be non-zero for a quadratic equation. The calculator handles real and complex roots.

5. Frequently Asked Questions (FAQ)

Q1: What if a = 0?
A: If a = 0, the equation becomes linear (bx + c = 0) and has only one root: x = -c/b.

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

Q3: What's the geometric interpretation?
A: The roots represent the x-intercepts of the parabola y = ax² + bx + c. Complex roots mean the parabola doesn't intersect the x-axis.

Q4: How precise are the results?
A: Results are rounded to 4 decimal places for clarity, but calculations use full precision.

Q5: Can I use fractions or decimals?
A: The calculator accepts decimal inputs. For fractional coefficients, convert them to decimal form first.