1. What Is The Solution Set Calculator?

The Solution Set Calculator finds the roots or solutions to quadratic equations of the form ax² + bx + c = 0. It calculates real and complex solutions using the quadratic formula.

2. How Does The Calculator Work?

The calculator uses the quadratic formula:

Where:

• \( a \) — Coefficient of x² (cannot be zero)
• \( b \) — Coefficient of x
• \( c \) — Constant term

Explanation: The discriminant (b² - 4ac) determines the nature of the roots:

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

3. Importance Of Finding Solution Sets

Details: Finding solution sets is fundamental in algebra and has applications in physics, engineering, economics, and many other fields where quadratic relationships occur.

4. Using The Calculator

Tips: Enter the coefficients a, b, and c from your quadratic equation. Ensure coefficient a is not zero. The calculator will display the solution set based on the discriminant value.

5. Frequently Asked Questions (FAQ)

Q1: What if the discriminant is negative?
A: The equation has no real solutions but two complex conjugate roots involving imaginary numbers.

Q2: Can coefficient a be zero?
A: No, if a = 0, the equation becomes linear (bx + c = 0), not quadratic.

Q3: What are the applications of quadratic equations?
A: Quadratic equations model projectile motion, area problems, profit maximization, and many real-world phenomena.

Q4: How accurate are the solutions?
A: Solutions are calculated with high precision, typically rounded to 4 decimal places for clarity.

Q5: Can this calculator handle complex numbers?
A: This version displays when solutions are complex but doesn't show the complex number format. For complex solutions, specialized calculators are recommended.