Help With Correspondence Course: Factored Form Equation for Family of Functions

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  • Thread starter Thread starter Erin_Sharpe
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SUMMARY

The discussion centers on writing an equation in factored form for a family of functions with non-repeated zeros at 3, 0, -9 + 4i, and -9 - 4i. The general formula provided is y(x) = a(x - x₁)(x - x₂)(x - x₃)(x - x₄), where "a" is a non-zero parameter representing the family of functions, and x₁, x₂, x₃, and x₄ are the specified roots. This formula allows for the construction of specific polynomial equations based on the given roots.

PREREQUISITES
  • Understanding of polynomial functions and their properties
  • Familiarity with complex numbers and their representation
  • Knowledge of factored form equations in algebra
  • Basic grasp of parameters in mathematical functions
NEXT STEPS
  • Study the concept of polynomial roots and their significance in function behavior
  • Learn about complex conjugates and their role in polynomial equations
  • Explore the impact of the parameter "a" on the shape of polynomial graphs
  • Practice writing factored form equations for various sets of roots
USEFUL FOR

Students in algebra courses, educators teaching polynomial functions, and anyone preparing for advanced mathematics programs who require a solid understanding of factored form equations.

Erin_Sharpe
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I'm taking a correspondence course to upgrade my marks for admission to a program.. and since its all teach yourself, I'm having some trouble on this particular question:

Write an equation in factored form for the family of functions having non-repeated zeros at 3, 0, -9 +4i and -9-4i

AND

write in factored form, the equation of a specific member of this family of functions.


Keep in mind guys that I'm not trying to do my homework on here, I just could really use some help!
Thanks!
Erin
 
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I'll give u the general formula
[tex]y(x)=a(x-x_{1})(x-x_{2})(x-x_{3})(x-x_{4})[/tex]
,where "a" is a parameter (the one that gives the idea of 'family of functions'),and [itex]x_{i}[/itex] are the roots of the polynomial 'y',else,the zero-s of the function 'y'.

It's good if [itex]a\neq 0[/itex].

Daniel.
 
Thank you! Thank you!
 

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