Write The Equation That Has The Following Zeros Calculator

This calculator helps you find the polynomial equation that has specific zeros (roots). Simply enter the zeros of the equation, and the calculator will generate the corresponding polynomial equation in both factored and expanded forms.

How to Use This Calculator

Using the calculator is simple:

Enter the zeros of the equation in the input field. Separate multiple zeros with commas.
Click the "Calculate" button to generate the polynomial equation.
Review the results, which include both the factored form and the expanded form of the equation.
Use the "Reset" button to clear the inputs and start over.

The calculator will display the polynomial equation in the form (x - r₁)(x - r₂)...(x - rₙ) = 0, where r₁, r₂, ..., rₙ are the zeros you entered. It will also show the expanded form of the equation.

How It Works

To find the polynomial equation with given zeros, we use the fact that if r is a zero of a polynomial, then (x - r) is a factor of the polynomial. Therefore, if the zeros are r₁, r₂, ..., rₙ, the polynomial can be written as:

(x - r₁)(x - r₂)...(x - rₙ) = 0

This is the factored form of the equation. To get the expanded form, we multiply the factors together to obtain a single polynomial equation in standard form.

Note

This method works for polynomials with real or complex zeros. For complex zeros, the calculator will display them in the form a + bi.

Examples

Example 1: Simple Zeros

Suppose the zeros of the equation are 2 and -3. The factored form of the equation is:

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

The expanded form is:

x² + x - 6 = 0

Example 2: Complex Zeros

If the zeros are 1 + i and 1 - i (where i is the imaginary unit), the factored form is:

(x - (1 + i))(x - (1 - i)) = 0

The expanded form is:

x² - 2x + 2 = 0

FAQ

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

The factored form shows the polynomial as a product of its factors, which correspond to its zeros. The expanded form is a single polynomial expression in standard form, which is often easier to work with for solving or graphing.

Can I use this calculator for equations with more than two zeros?

Yes, you can enter as many zeros as you need. The calculator will generate the corresponding polynomial equation with all the zeros you provide.

What if I enter a zero that is not a real number?

The calculator can handle complex zeros. It will display them in the form a + bi and generate the appropriate polynomial equation.