How to solve an $n$-th degree polynomial equation
In fact, it is known that only a very small part of polynomials of degree $\ge 5$ admit a solution formula using the operations listed above. Nevertheless, finding solutions to polynomial formulas is quite easy using numerical methods, e.g., Newton's method. These methods are independent of the degree of the polynomial.
SOLUTION: How do you find an nth-degree polynomial function …
That means that if is a zero, then is also a zero of the desired polynomial function. If is a zero of a polynomial function in , then is a factor of the polynomial. A family of polynomial functions of the form: all have the same zeros. So we know the following things: 1. The desired polynomial function has exactly 3 zeros. 2. The zeros are ...
Polynomial nth derivative - Mathematics Stack Exchange
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Is there a simpler way to prove that the nth difference of a degree …
2020年7月3日 · Upon trying to prove this myself, I've found that the nth difference= $$\sum_{r=0}^{n}{n \choose r}(\sum_{p=0}^{n}a_p(c-r)^{n-p})*(-1)^r$$ Where f(X) is a polynomial and f(c-r)= $$\sum_{p=0}^{n}a_p(c-r)^{n-p}$$ I've tried proving this, but I …
Find N degree polynomial from N+1 points
2014年2月22日 · $\begingroup$ "And you can even make the stronger statement that the resulting polynomial is degree n" This was my question actually. "Does this mean that given any set of n+1 points, there exists a polynomial of degree n that passes through all of them?" Nice answer though! +1 $\endgroup$ –
Finding nth degree polynomial functions - Mathematics Stack …
2013年4月26日 · I need to find an nth degree polynomial function that has real coefficients using the following conditions: n=3; 3 and 4i are zeros; f(2)=40. I have no idea what I'm doing on this one. It's been too long. Also, there's no homework tag because this isn't something I have to do. I'm just brushing up in preparation for an upcoming math course.
how to memorize the sum and product of roots for an $n^{th}
2019年3月24日 · However the important thing to observe from the above series is that the alternate negative fraction (starting from the 1st -ve term) of each successive term with that of the first term of the polynomial is equal to the sum of the …
functions - Why does an $n$th degree polynomial have at most …
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numerical methods - nth degree interpolating polynomials
An interpolating polynomial is one that goes exactly through the points of interest. As two points determine a line, a degree one interpolating polynomial can only go through two points (unless there is an accident and another point is on the same line.)
Finding an nth degree polynomial. - Mathematics Stack Exchange
2015年5月20日 · Finding an nth degree polynomial. Ask Question Asked 9 years, 6 months ago. Modified 9 years, 6 months ago.