October 26th, 2012, 02:14 PM  #1 
Newbie Joined: Oct 2012 Posts: 5 Thanks: 0  Finding Real Roots of an Equation
Hey anyone, and everyone. I was having a little trouble with a problem. What are the steps needed to find how many real roots x^(5)+5x+4=0 Help would be great yall! thx 
October 26th, 2012, 03:01 PM  #2 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,234 Thanks: 190  Re: Finding Real Roots of an Equation
The first thing to do as a beginner is graph it. If you're not allowed to graph it use descarte's rule of signs. http://www.purplemath.com/modules/drofsign.htm Other things to note. The coefficients 1, 5, 4 are real and the powers are natural numbers, the highest power odd so there is at least 1 real root. For these particular conditions satisfied means complex roots occur in conjugate pairs so the number of real solutions can be 1, 3, or 5 however, descarte's rule of signs tells us there is only 1 negative real root and no positive real roots. 

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