What are Vieta's Formulas in Polynomial Functions?

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SUMMARY

Vieta's formulas establish a direct relationship between the coefficients of a polynomial and the sums and products of its roots. This discussion highlights three methods for solving polynomial equations: finding roots directly, applying Vieta's formulas, and expanding factored forms like (x - 1)(x - 1/α) = 0. The participants emphasize the utility of Vieta's formulas in simplifying the process of determining polynomial roots without extensive calculations.

PREREQUISITES
  • Understanding of polynomial functions
  • Familiarity with algebraic expressions
  • Basic knowledge of roots and coefficients in equations
  • Ability to expand and factor polynomials
NEXT STEPS
  • Study Vieta's formulas in detail and their applications in polynomial equations
  • Learn how to derive roots of polynomials using numerical methods
  • Explore polynomial factoring techniques and their significance
  • Investigate the relationship between polynomial coefficients and their graphical representations
USEFUL FOR

Students, educators, and mathematicians interested in polynomial functions, algebra, and the application of Vieta's formulas in solving equations.

mathland
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I say the answer is A.

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Did you check it? Did the roots come out? (They don't.)

There are three ways to do this one.
1) Cheat and find the roots of all your possible answers.

2) Use the Vieta formulas.

3) Write out [math](x - 1) \left ( x - \dfrac{1}{ \alpha } \right ) = 0[/math] and expand.

-Dan
 
topsquark said:
Did you check it? Did the roots come out? (They don't.)

There are three ways to do this one.
1) Cheat and find the roots of all your possible answers.

2) Use the Vieta formulas.

3) Write out [math](x - 1) \left ( x - \dfrac{1}{ \alpha } \right ) = 0[/math] and expand.

-Dan

No. I did not check it. What is the Vieta formulas?
 
Beer soaked ramblings follow.
mathland said:
No. I did not check it. What is the Vieta formulas?
Translation: I don't know man. That sounds like a lot of work!
 
mathland said:
No. I did not check it. What is the Vieta formulas?

Vieta's formulas are equations that connect some expressions of the roots of a polynomial equation to its coefficients. (See e.g. wikipedia)
 
Theia said:
Vieta's formulas are equations that connect some expressions of the roots of a polynomial equation to its coefficients. (See e.g. wikipedia)

I'll need to look that up.
 

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