Find the Polynomial Given the Zeros Calculator
Finding a polynomial given its zeros is a fundamental concept in algebra. It’s crucial for understanding the relationship between the roots and coefficients of a polynomial equation.
- Enter the zeros of the polynomial separated by commas in the ‘Zeros’ field.
- Select the degree of the polynomial from the dropdown menu.
- Click the ‘Calculate’ button to find the polynomial.
The formula to find a polynomial given its zeros is:
P(x) = a * (x – r1) * (x – r2) * … * (x – rn)
where ‘a’ is the leading coefficient, and ‘rn’ are the roots of the polynomial.
| Degree | Zeros | Polynomial |
|---|---|---|
| 1 | -2 | x + 2 |
| 2 | -2, 3 | x^2 – x – 6 |
- Always ensure the degree of the polynomial is correct to avoid incorrect results.
- If the leading coefficient is not 1, you can multiply the entire polynomial by that value to get the correct form.
What if I don’t know the leading coefficient?
If you don’t know the leading coefficient, you can still find the polynomial by assuming it’s 1. The calculator will output the polynomial in this form.
For more information, see the following authoritative sources: