1. What is the Quadratic Equation?

The quadratic equation describes a parabola and has the standard form ax² + bx + c = 0. Its solutions (roots) can be found using the quadratic formula, which may yield real or complex numbers.

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
• \( \sqrt{b^2 - 4ac} \) — Discriminant (determines nature of roots)

Explanation: The calculator first computes the discriminant, then determines whether roots are real or complex, and finally converts decimal solutions to fractional form when possible.

3. Solving with Fractions

Details: The calculator attempts to convert decimal solutions to exact fractions using a continued fraction algorithm, which is particularly useful when working with fractional coefficients.

4. Using the Calculator

Tips: Enter coefficients as decimals or fractions (e.g., 0.5 or 1/2). The calculator accepts any real numbers for a, b, and c (with a ≠ 0).

5. Frequently Asked Questions (FAQ)

Q1: Why does the calculator show complex numbers?
A: When the discriminant (b² - 4ac) is negative, the equation has complex roots involving imaginary numbers.

Q2: How accurate is the fraction conversion?
A: The conversion is accurate to 6 decimal places. Very precise decimals may not convert to simple fractions.

Q3: Can I use this for linear equations?
A: No, this is specifically for quadratic equations (a ≠ 0). For linear equations (a = 0), use a different solver.

Q4: How does this compare to Desmos?
A: This provides exact fractional solutions while Desmos typically shows decimal approximations.

Q5: What about irrational roots?
A: Irrational roots (like √2) will be shown as decimals with fractional approximations.