How do you find the lowest degree of a polynomial function?
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How do you find the lowest degree of a polynomial function?
If a polynomial of lowest degree p has zeros at x=x1,x2,…,xn x = x 1 , x 2 , … , x n , then the polynomial can be written in the factored form: f(x)=a(x−x1)p1(x−x2)p2⋯(x−xn)pn f ( x ) = a ( x − x 1 ) p 1 ( x − x 2 ) p 2 ⋯ ( x − x n ) p n where the powers pi on each factor can be determined by the behavior of the graph …
What polynomial function has a degree of 1?
Linear function
Polynomial Functions
| Degree of the polynomial | Name of the function |
|---|---|
| 0 | Constant function |
| 1 | Linear function |
| 2 | Quadratic function |
| 3 | Cubic function |
What is the lead coefficient of a polynomial?
The highest power of the variable that occurs in the polynomial is called the degree of a polynomial. The leading term is the term with the highest power, and its coefficient is called the leading coefficient.
What is a function with degree 1?
Degree 1: a linear function. Degree 2: quadratic. Degree 3: cubic. Degree 4: quartic or biquadratic.
What is the polynomial function of lowest degree with lead coefficient?
The polynomial function of lowest degree with lead coefficient 1 and roots 1 and 1 + i is f(x) = x3 – 3×2 + 4x – 2.
What is the polynomial function of the lowest degree with lead coefficient 1 and roots i 2 and 2?
The polynomial function of lowest degree with lead coefficient 1 and roots i, -2, and 2 is f(x) =x4 – 3×2 – 4.
What is second degree polynomial function FX?
quadratic function
A quadratic function is a second degree polynomial function. The general form of a quadratic function is this: f (x) = ax2 + bx + c, where a, b, and c are real numbers, and a≠ 0.
How to find the lowest degree polynomial with leading coefficient?
Given the roots of the polynomial function. we have to find the lowest degree polynomial with leading coefficient 1 and roots i, –2, and 2. By complex conjugate root theorem which states that if P is the polynomial and a+ib is a root of P with a and b real numbers, then its complex conjugate a-ib is also a root of that polynomial P.
How do you find the root of a polynomial function?
By complex conjugate root theorem which states that if P is the polynomial and a+ib is a root of P with a and b real numbers, then its complex conjugate a-ib is also a root of that polynomial P. ∴ -i is also the root of the polynomial function.
What is the value of 1+i for a polynomial?
All complex roots come in pairs, so 1+i must be a root as well. Therefore the polynomial equals (x-1) (x-1-i) (x-1+i). I’m feeling too lazy to multiply that out, but do it and you’re done