1. What is the Quadratic Formula?

The quadratic formula calculates the roots of any quadratic equation in the form ax² + bx + c = 0. It provides solutions for x that satisfy the equation, whether they are real or complex numbers.

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
• \( \sqrt{b^2 - 4ac} \) — Discriminant (determines nature of roots)

Explanation: The discriminant (b² - 4ac) determines whether the roots are real and distinct (positive), real and equal (zero), or complex conjugates (negative).

3. Importance of Quadratic Roots

Details: Finding roots of quadratic equations is fundamental in algebra, physics, engineering, and many scientific applications. Roots represent x-intercepts of the parabola graph.

4. Using the Calculator

Tips: Enter coefficients a, b, and c of your quadratic equation. The calculator will display both roots, whether real or complex. Coefficient a cannot be zero.

5. Frequently Asked Questions (FAQ)

Q1: What if I get complex roots?
A: Complex roots occur when the discriminant is negative, meaning the parabola doesn't intersect the x-axis. They come in conjugate pairs (a ± bi).

Q2: What does a double root mean?
A: A double root occurs when the discriminant is zero, meaning the parabola touches the x-axis at exactly one point (its vertex).

Q3: Why can't coefficient a be zero?
A: If a=0, the equation becomes linear (bx + c = 0), not quadratic. The quadratic formula doesn't apply in this case.

Q4: How precise are the results?
A: Results are rounded to 4 decimal places. For exact symbolic solutions, algebraic manipulation may be needed.

Q5: Can I use this for higher-degree polynomials?
A: No, this calculator only solves quadratic equations. Cubic and quartic equations require different formulas.