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

Explanation: The term under the square root (b² - 4ac) is called the discriminant. It 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 essential for solving many real-world problems.

4. Using the Calculator

Tips: Enter the coefficients a, b, and c from your quadratic equation. The calculator will display both solutions (real or complex). Remember that 'a' cannot be zero in a quadratic equation.

5. Frequently Asked Questions (FAQ)

Q1: What if I get complex roots?
A: Complex roots (with 'i') are valid mathematical solutions. They indicate the parabola doesn't intersect the x-axis in real numbers.

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

Q4: Can I use fractions or decimals?
A: Yes, the calculator accepts both decimal and fractional inputs (like 0.5 or 1/2).

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