1. What is the Quadratic Formula?

The quadratic formula is a fundamental equation in algebra that provides the solutions to quadratic equations of the form ax² + bx + c = 0. It is also known as the X factor method for solving quadratic equations.

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

3. Importance of Quadratic Formula

Details: The quadratic formula is essential for solving second-degree polynomial equations and has applications in physics, engineering, economics, and various scientific fields where quadratic relationships occur.

4. Using the Calculator

Tips: Enter the coefficients a, b, and c from your quadratic equation. All values must be numerical, and coefficient a cannot be zero. The calculator will provide both real and complex solutions as appropriate.

5. Frequently Asked Questions (FAQ)

Q1: What if the discriminant is negative?
A: When the discriminant (b² - 4ac) is negative, the solutions are complex numbers involving the imaginary unit i (√-1).

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

Q3: What does the ± symbol mean?
A: The ± indicates that there are two solutions: one using the positive square root and one using the negative square root.

Q4: When are both solutions the same?
A: When the discriminant equals zero, both solutions are identical, resulting in one real solution (a repeated root).

Q5: Can this formula solve all quadratic equations?
A: Yes, the quadratic formula can solve any quadratic equation, whether the roots are real or complex.