Write A Polynomial From The Roots Given Below Calculator

This calculator helps you construct a polynomial equation from its given roots. Simply enter the roots of the polynomial, and the calculator will generate the polynomial in standard form.

How to Use This Calculator

Using the polynomial from roots calculator is straightforward:

Enter the roots of the polynomial in the input field. Separate multiple roots with commas.
Click the "Calculate" button to generate the polynomial equation.
Review the result, which will be displayed 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.

How It Works

The polynomial from roots calculator uses the fundamental theorem of algebra, which states that a polynomial of degree n has exactly n roots (including multiplicities). The calculator constructs the polynomial by multiplying linear factors corresponding to each root.

For roots \( r_1, r_2, \ldots, r_n \), the polynomial is:

\( P(x) = (x - r_1)(x - r_2) \cdots (x - r_n) \)

This formula is implemented in the calculator to generate the polynomial equation from the given roots.

Example Calculation

Let's say you have roots at \( x = 2 \) and \( x = -3 \). The polynomial would be:

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

Expanding this gives:

\( P(x) = x^2 + x - 6 \)

Using the calculator, you would enter "2, -3" in the input field and get the same result.

Frequently Asked Questions

What if I have complex roots?

The calculator can handle complex roots. Simply enter them in the format "a+bi" for complex numbers. The polynomial will be generated accordingly.

Can I use repeated roots?

Yes, the calculator can handle repeated roots. Enter the same root multiple times separated by commas to indicate multiplicity.

What if I enter non-numeric values?

The calculator will display an error message if you enter non-numeric values. Please ensure all inputs are valid numbers or complex numbers in the correct format.