Roots & Product of ax^2 + bx + c = 0

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Discussion Overview

The discussion revolves around the properties of the roots of the quadratic equation ax^2 + bx + c = 0, specifically focusing on the sum and product of the roots. Participants explore different methods to derive these properties, including the use of the quadratic formula and factorization techniques.

Discussion Character

  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant requests a proof that the sum of the roots is -b/a and the product is c/a.
  • Another participant asks if others are familiar with the quadratic formula, implying its relevance to the discussion.
  • A different participant suggests that knowing the roots is unnecessary and proposes using standard results about polynomial factorization to approach the problem.
  • Another participant provides a specific factorization approach, stating that if u and v are the roots, the equation can be expressed as a(x - u)(x - v) and suggests comparing coefficients to derive the desired results.

Areas of Agreement / Disagreement

There is no consensus on a single method to prove the properties of the roots, as participants present different approaches and perspectives on the necessity of knowing the roots.

Contextual Notes

Some assumptions about the familiarity with polynomial factorization and the quadratic formula are present, but these are not explicitly stated by all participants. The discussion does not resolve the mathematical steps involved in deriving the properties of the roots.

rhule009
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Prove that the sum of the roots and product of the roots of the equation
ax^2 + bx + c = 0 are
-b/a and c/a respectively
thank you
 
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Do you know what the quadratic formula is?
 
You don't need that. You dont' need to know what the roots are at all. You can let them be r and s, and just use standard results such as if r is a root of f(x), then f(x) = (x-r)g(x) for some g(x). I.e. just factorize the equation.
 
If u and v are roots of that equation then
[tex]ax^2+ bx+ c= a(x- u)(x- v)[/itex]<br /> Multiply the right side and compare corresponding coefficients.[/tex]
 

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