Find Positive Negative and Complex Zeros Calculator

What are zeros of a polynomial?

The zeros of a polynomial are the solutions to the equation P(x) = 0, where P(x) is a polynomial function. For example, in the equation x² - 5x + 6 = 0, the zeros are x = 2 and x = 3.

Zeros can be classified as:

• Positive zeros: Solutions greater than zero
• Negative zeros: Solutions less than zero
• Complex zeros: Solutions that are complex numbers (involving i, the imaginary unit)

Finding zeros is fundamental in algebra and has applications in physics, engineering, and other fields.

How to find zeros of a polynomial

For quadratic equations (degree 2)

Use the quadratic formula:

Where a, b, and c are coefficients of the quadratic equation ax² + bx + c = 0.

For higher-degree polynomials

Methods include:

• Factoring
• Synthetic division
• Numerical methods (like Newton-Raphson)
• Graphical methods

This calculator uses numerical methods to approximate zeros for polynomials of any degree.

Using the calculator

Enter the coefficients of your polynomial in the calculator on the right. The calculator will find all real and complex zeros of the polynomial.

For example, to solve x³ - 6x² + 11x - 6 = 0, you would enter:

• Coefficient a₃ = 1
• Coefficient a₂ = -6
• Coefficient a₁ = 11
• Coefficient a₀ = -6

The calculator will display all zeros of the polynomial, including positive, negative, and complex solutions.

Example calculation

Let's find the zeros of the polynomial x³ - 6x² + 11x - 6 = 0.

Using the calculator:

1. Enter coefficients: a₃=1, a₂=-6, a₁=11, a₀=-6
2. Click "Calculate"
3. The calculator will display the zeros: x = 1, x = 2, x = 3

These are all real, positive zeros of the polynomial.