Find the cubic polynomial satisfying f(0) = -5, f(1) = 0, f(2) = 15, f(3) = 52.?

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    Cubic Polynomial
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Discussion Overview

The discussion revolves around finding a cubic polynomial that satisfies specific conditions: f(0) = -5, f(1) = 0, f(2) = 15, and f(3) = 52. The scope includes mathematical reasoning and problem-solving approaches.

Discussion Character

  • Mathematical reasoning, Debate/contested

Main Points Raised

  • One participant claims the correct polynomial is 2x^3 - x^2 + 4x - 5.
  • Another participant suggests using Lagrange interpolation polynomials as a method to find the solution.
  • A different participant proposes translating the problem into a set of linear equations to determine the coefficients of the polynomial.
  • One participant notes that the choice between solving a system of linear equations or directly writing down the answer is subjective.

Areas of Agreement / Disagreement

Participants present multiple competing views on how to approach the problem, with no consensus on a single method being preferred.

Contextual Notes

Participants express different methods for solving the problem, indicating that assumptions about preferred techniques may vary. The discussion does not resolve which method is superior or more effective.

escobar147
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Here is the correct answer: 2x^3 - x^2 + 4x - 5

My attempt only gives me one cubed term and the other terms are also marginally off, any help on who can show me how to get the correct answer will be hugely appreciated
 
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Hi there,

What you really need is to translate the problem into a set of linear equations. If you let f(x)=ax3+bx2+cx+d, then f(0)=-5 gives d=-5, f(1)=0 gives a+b+c+d=0 etc, and you can quickly find the correct values of a, b, c and d.
 
I guess it is a matter of taste as to whether one prefers to solve a system of linear equations or to just write down the answer.
 

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