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May 28th, 2010, 11:27 AM  #1 
Newbie Joined: May 2010 Posts: 3 Thanks: 0  Finding Polynomial with Roots of Real and Complex Numbers
Find the polynomial of lowest degree with rational coefficients that has 2 and 3+5i as two of its roots.

May 28th, 2010, 05:51 PM  #2  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Re: Finding Polynomial with Roots of Real and Complex Numbers Hello, HFH! Quote:
Complex roots occur in conjugate pairs. Since is a root, then is also a root. Hence:[color=beige] .[/color] are factors of the polynomial. The simplest polynmial is:[color=beige] .[/color] [color=beige]. . . . . . . . . . . . . . . . . . [/color]  
May 29th, 2010, 07:47 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,931 Thanks: 2205 
Equations have roots; polynomials (and other functions) have zeros.

May 29th, 2010, 01:19 PM  #4  
Global Moderator Joined: May 2007 Posts: 6,807 Thanks: 716  Re: Quote:
 

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complex, finding, numbers, polynomial, real, roots 
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