1. What is the Quadratic Formula?

The quadratic formula provides solutions to quadratic equations of the form ax² + bx + c = 0. It is derived by completing the square and gives both real and complex solutions based on the discriminant value.

2. How Does the Calculator Work?

The calculator uses the quadratic formula:

Where:

• \( a \) — Coefficient of x² term (cannot be zero)
• \( b \) — Coefficient of x term
• \( c \) — Constant term
• \( \pm \) — Indicates two possible solutions

Explanation: The discriminant (b² - 4ac) determines the nature of the solutions. Positive discriminant gives two real solutions, zero gives one real solution, and negative gives two complex solutions.

3. Importance of Quadratic Solutions

Details: Solving quadratic equations is fundamental in mathematics, physics, engineering, and many other fields. The solutions represent x-intercepts of parabolas and have practical applications in optimization problems.

4. Using the Calculator

Tips: Enter coefficients a, b, and c as real numbers. Coefficient a must be non-zero. The calculator will display both solutions (real or complex) with four decimal precision.

5. Frequently Asked Questions (FAQ)

Q1: What if the discriminant is negative?
A: The calculator will display complex solutions in the form a ± bi, where i is the imaginary unit (√-1).

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

Q3: What is the geometric interpretation?
A: The solutions represent the x-coordinates where the parabola y = ax² + bx + c intersects the x-axis.

Q4: Are there other methods to solve quadratics?
A: Yes, including factoring, completing the square, and graphical methods, but the quadratic formula works for all cases.

Q5: How accurate are the results?
A: Results are calculated with floating-point precision and rounded to four decimal places for readability.