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June 26th, 2012, 12:37 PM  #1 
Member Joined: Apr 2012 Posts: 92 Thanks: 0  Polynomial help
I would like to clarify one thing, in questions like, Find all third degree real polynomials with zeros of 1/2 and 1 3i there's always this constant multiplied to the answer, such that the polynomial f(x) = a(answer). What and why is there a need for a constant to be multiplied? In a general polynomial like 3x^2+x+5, I don't see the need for existence of a constant, unless the constant is 1. Thank you! 
June 26th, 2012, 12:50 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Polynomial help
Consider that the roots are not changed when multiplying the polynomial by a constant but the polynomial is changed. For instance: Yet, the two binomials have the same root. 
June 26th, 2012, 01:07 PM  #3  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Re: Polynomial help Hello, Tutu! Quote:
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June 26th, 2012, 01:10 PM  #4 
Member Joined: Apr 2012 Posts: 92 Thanks: 0  Re: Polynomial help
I see now, thank you thank you thank you!


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