Highest degree of a given polynomial is

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Homework Help Overview

The discussion revolves around determining the minimum degree of a polynomial given specific values at certain points: p(0)=5, p(1)=4, p(2)=9, and p(3)=20. Participants are exploring the implications of these values on the polynomial's degree.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to assess the feasibility of connecting the given points with polynomials of varying degrees, specifically questioning the possibility for first and second degree polynomials. There is confusion regarding the implications of options for higher degree polynomials.

Discussion Status

Some participants have provided reasoning for why a first or second degree polynomial may not be sufficient, while others suggest a method of checking through differences to explore the polynomial's degree further. The discussion is ongoing with no clear consensus yet.

Contextual Notes

There is an indication that participants are unsure about the definitions and implications of polynomial degrees in relation to the provided points, and there may be constraints related to homework submission guidelines.

22990atinesh
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Homework Statement


A polynomial p(x) is such that p(0)=5, p(1)=4, p(2)=9 and p(3)=20. the minimum degree it can have
a) 1 b) 2 c) 3 d) 4

Homework Equations

The Attempt at a Solution


a) Not Possible can't connect these points using straight line
b) Not even possible to connect these points using 2 degree polynomial
I'm confused with options c) and d)
 
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22990atinesh said:

The Attempt at a Solution


a) Not Possible can't connect these points using straight line
b) Not even possible to connect these points using 2 degree polynomial
I'm confused with options c) and d)

not so fast...

If you want to know wether it's possible with 1st degree polynomial, compute the differences between consecutive numbers, if these are all the same, it is possible.
To do this for a 2nd degree polynomial, compute the differences between those differences, if these are all the same, it is possible. etc.
 
22990atinesh said:
b) Not even possible to connect these points using 2 degree polynomial
Please post your reasoning.
 

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