Polynomial Calculator From Roots

This polynomial calculator from roots helps you construct a polynomial equation when you know its roots. Whether you're a student studying algebra or a professional working with polynomial functions, this tool provides an easy way to generate the polynomial from its roots.

How to Use the Polynomial Calculator from Roots

Using our polynomial calculator from roots is simple. Follow these steps:

Enter the roots of the polynomial in the input field. Separate multiple roots with commas.
Click the "Calculate" button to generate the polynomial.
Review the result, which will display the polynomial in standard form.
Use the "Reset" button to clear the inputs and start over.

The calculator will handle both real and complex roots, providing the polynomial in its simplest form.

The Formula for Constructing Polynomials from Roots

To construct a polynomial from its roots, you can use the following formula:

P(x) = (x - r₁)(x - r₂)...(x - rₙ)

Where:

P(x) is the polynomial
r₁, r₂, ..., rₙ are the roots of the polynomial

This formula represents the polynomial as a product of linear factors, each corresponding to one of the roots.

For complex roots, the polynomial will include complex coefficients. The calculator will display the polynomial in its standard form, including any necessary imaginary components.

Example Calculation

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

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

Expanding this product gives:

P(x) = x³ - 4x² + 5x - 6

This is the polynomial that has roots at 2, -1, and 3.

Frequently Asked Questions

Can this calculator handle complex roots?

Yes, the calculator can handle complex roots. It will display the polynomial with complex coefficients in standard form.

What if I have repeated roots?

The calculator will automatically account for repeated roots by including the appropriate powers in the polynomial.

Can I use negative roots?

Yes, you can enter negative roots. The calculator will correctly handle them in the polynomial construction.