1. What Is The Quadratic Formula?

The quadratic formula provides the solutions to any quadratic equation of the form ax² + bx + c = 0. It is one of the most fundamental formulas in algebra and is derived from completing the square.

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

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

3. Importance Of Quadratic Equations

Details: Quadratic equations appear in various fields including physics, engineering, economics, and computer graphics. They describe parabolic motion, optimization problems, and many natural phenomena.

4. Using The Calculator

Tips: Enter the coefficients a, b, and c from your quadratic equation. The calculator will provide real or complex solutions based on the discriminant value.

5. Frequently Asked Questions (FAQ)

Q1: What if the discriminant is negative?
A: When the discriminant is negative, the equation has two complex solutions involving imaginary numbers.

Q2: What if coefficient a is zero?
A: If a = 0, the equation is not quadratic but linear. The calculator will return an error in this case.

Q3: How many decimal places are shown?
A: Solutions are rounded to 4 decimal places for readability while maintaining reasonable precision.

Q4: Can this solve equations with fractions?
A: Yes, you can enter fractional values as decimals, or the calculator will accept exact fractions if converted to decimal form.

Q5: What are some real-world applications?
A: Quadratic equations model projectile motion, profit maximization, bridge design, and many optimization problems in various fields.