Does the function f(x) = ax+b have a discriminant? If so, what is it?

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Discussion Overview

The discussion revolves around whether the linear function f(x) = ax + b has a discriminant, and if so, what that discriminant would be. The scope includes theoretical considerations and references to mathematical definitions.

Discussion Character

  • Debate/contested

Main Points Raised

  • Some participants question if a discriminant exists for a first-degree function, noting that standard definitions typically apply to polynomials of higher degrees.
  • References to Wikipedia articles are made, indicating that the discriminant is not explicitly defined for first-degree functions.
  • One participant suggests working out the Sylvester matrix and dividing by a as a potential method to derive a discriminant.
  • Another participant proposes that based on their calculations, the discriminant is 1, but this claim is not universally accepted.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether a discriminant exists for the function f(x) = ax + b, and multiple competing views remain regarding its definition and value.

Contextual Notes

Limitations include the lack of clarity on how the discriminant is defined for first-degree polynomials and the dependence on interpretations of existing mathematical literature.

Jhenrique
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f(x) = ax+b has discriminant? If yes, which is?
 
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Jhenrique said:
Nothing is said about the function of 1st degree...

So?...

They talk about polynomials of degree ##n##. So set ##n=1##.
 
Second my calculus, the discriminant is 1. Correct?
 

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