1. What is the Quadratic Formula?

The quadratic formula provides the solutions to quadratic equations of the form ax² + bx + c = 0. It is derived by completing the square and 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 term under the square root (b² - 4ac) is called the discriminant and 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 many areas of mathematics, physics, engineering, and economics. They describe parabolic relationships and are fundamental in algebra.

4. Using the Calculator

Tips: Enter the coefficients a, b, and c from your quadratic equation. The calculator will display real or complex solutions as appropriate.

5. Frequently Asked Questions (FAQ)

Q1: What if I get complex solutions?
A: Complex solutions indicate the parabola doesn't intersect the x-axis. The solutions are still mathematically valid.

Q2: Why can't coefficient a be zero?
A: If a=0, the equation becomes linear (bx + c = 0), not quadratic.

Q3: How accurate are the solutions?
A: Solutions are calculated to high precision but displayed rounded to 4 decimal places.

Q4: Can I solve equations with fractions or decimals?
A: Yes, the calculator accepts decimal coefficients.

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