My Math Forum Finding Polynomial with Roots of Real and Complex Numbers

 Algebra Pre-Algebra and Basic Algebra Math Forum

 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:
 Find the polynomial of lowest degree with rational coefficients that has $-2$ and $-3+5i$ as two of its roots.

Complex roots occur in conjugate pairs.
Since $-3+5i$ is a root, then $-3-5i$ is also a root.

Hence:[color=beige] .[/color]$(x+2),\;\left(x-[-3+5i]\right),\;\left(x-[-3-5i]\right)\,$ are factors of the polynomial.

The simplest polynmial is:[color=beige] .[/color]$f(x) \;=\;(x\,+\,2)(x\,+\,3\,-\,5i)(x\,+\,3\,+\,5i)$

[color=beige]. . . . . . . . . . . . . . . . . . [/color]$f(x) \;=\;x^3\,+\,8x^2\,+\,46x\,+\,68$

 May 29th, 2010, 07:47 AM #3 Global Moderator   Joined: Dec 2006 Posts: 20,471 Thanks: 2038 Equations have roots; polynomials (and other functions) have zeros.
May 29th, 2010, 01:19 PM   #4
Global Moderator

Joined: May 2007

Posts: 6,730
Thanks: 689

Re:

Quote:
 Originally Posted by skipjack Equations have roots; polynomials (and other functions) have zeros.
You're quibbling.

 Tags complex, finding, numbers, polynomial, real, roots

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post panky Algebra 1 December 10th, 2013 07:15 AM TsAmE Complex Analysis 4 October 19th, 2010 08:48 PM nisko Complex Analysis 2 November 6th, 2008 08:52 AM domaPL Real Analysis 1 January 12th, 2008 10:28 AM domaPL Number Theory 0 December 31st, 1969 04:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top