Polynomial Generator From Roots Calculator

This polynomial generator from roots calculator helps you create a polynomial equation from its roots. Simply enter the roots of the polynomial, and the calculator will generate the corresponding polynomial equation. The calculator also provides a visualization of the roots on a graph for better understanding.

What is a Polynomial Generator from Roots?

A polynomial generator from roots is a tool that creates a polynomial equation based on its roots. Polynomials are mathematical expressions consisting of variables and coefficients, combined using addition, subtraction, multiplication, and non-negative integer exponents. The roots of a polynomial are the values of the variable that make the polynomial equal to zero.

For example, if you have roots at x = 2 and x = -3, the polynomial generator will produce the equation (x - 2)(x + 3) = 0, which can be expanded to x² + x - 6 = 0.

Note: The polynomial generator from roots assumes that the roots are real numbers. Complex roots are not supported in this calculator.

How to Use the Calculator

Enter the roots of the polynomial in the input field. Separate multiple roots with commas.
Click the "Calculate" button to generate the polynomial equation.
The calculator will display the polynomial equation and a visualization of the roots on a graph.
To reset the calculator, click the "Reset" button.

Formula Used

The polynomial generator from roots uses the following formula to create the polynomial equation:

If the roots of the polynomial are r₁, r₂, ..., rₙ, then the polynomial equation is:

(x - r₁)(x - r₂)...(x - rₙ) = 0

This formula represents the factored form of the polynomial equation. The roots are the values of x that make the equation equal to zero.

Worked Example

Let's say you have roots at x = 1, x = -2, and x = 3. Using the formula:

(x - 1)(x + 2)(x - 3) = 0

Expanding this equation gives:

x³ - 2x² - 5x + 6 = 0

So, the polynomial equation is x³ - 2x² - 5x + 6 = 0.

FAQ

Can I use complex roots with this calculator?

No, this calculator only supports real roots. Complex roots are not supported.

How do I enter multiple roots?

Separate multiple roots with commas in the input field. For example, "1, -2, 3".

What is the difference between the factored form and expanded form of a polynomial?

The factored form of a polynomial shows the roots as factors, while the expanded form combines these factors into a single polynomial equation. The calculator provides both forms for your convenience.