- #1
lucifer_x
- 15
- 0
how would i write the depressed polynomial for the obvious root of
f(x) = x5 - .5x4 - 5.5x3 - 3.5x2 - 6.5x - 3
f(x) = x5 - .5x4 - 5.5x3 - 3.5x2 - 6.5x - 3
Depressed polynomials are a type of polynomial in which the leading coefficient is equal to 1. This means that the polynomial is "depressed" or "simplified" compared to a standard polynomial, which has a leading coefficient of any number other than 1.
As mentioned before, the main difference between depressed polynomials and standard polynomials is that the leading coefficient of a depressed polynomial is always equal to 1. This simplifies the polynomial and makes it easier to work with in certain mathematical operations.
The leading coefficient being equal to 1 in depressed polynomials allows for easier factoring and finding the roots of the polynomial. It also simplifies the polynomial and makes it easier to graph and analyze.
Depressed polynomials are used in various areas of mathematics, such as algebra, calculus, and number theory. They are particularly useful in finding the roots of a polynomial and solving equations, as well as in polynomial interpolation and approximation.
Yes, any polynomial can be "depressed" by dividing all of its coefficients by the leading coefficient. This will result in a depressed polynomial with the same roots as the original polynomial.