Find Polynomial of Least Degree with Given Zeros Calculator
Find polynomial of least degree with given zeros is a crucial concept in algebra, with wide-ranging applications in mathematics, physics, and engineering. This calculator helps you find the polynomial of least degree that has specific given zeros.
- Enter the zeros of the polynomial, separated by commas.
- Select the degree of the polynomial.
- Click ‘Calculate’ to find the polynomial of least degree with the given zeros.
The formula used to find the polynomial is based on the Fundamental Theorem of Algebra and the Vieta’s formulas. The calculator uses these formulas to construct the polynomial.
Real-World Examples
1. Finding a quadratic polynomial: If you have a quadratic function that passes through the points (1, 2) and (3, 6), you can use this calculator to find the polynomial. Enter the zeros 1 and 3, and select the degree 2. The calculator will output the polynomial 2x – 1.
2. Finding a cubic polynomial: If you have a cubic function that passes through the points (1, 2), (2, 3), and (3, 4), you can use this calculator to find the polynomial. Enter the zeros 1, 2, and 3, and select the degree 3. The calculator will output the polynomial 3x^2 – 2x – 1.
| Degree | Polynomial | Zeros |
|---|---|---|
| 1 | 2x – 1 | 1 |
| 2 | 3x^2 – 2x – 1 | 1, 2 |
| 3 | 4x^3 – 3x^2 – 2x – 1 | 1, 2, 3 |
- Ensure the zeros you enter are distinct, as the calculator cannot handle repeated roots.
- If you’re unsure about the degree of the polynomial, start with a higher degree and decrease it until you find the polynomial of least degree.
What if I don’t know the degree of the polynomial?
If you’re unsure about the degree of the polynomial, start with a higher degree and decrease it until you find the polynomial of least degree.
Can this calculator handle repeated roots?
No, this calculator cannot handle repeated roots. If you have a repeated root, you’ll need to adjust your input to account for it.
For more information about polynomials, see the Math is Fun guide to polynomials.
To learn more about the Fundamental Theorem of Algebra, see the Encyclopedia of Mathematics entry.