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October 26th, 2012, 02:14 PM   #1
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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
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October 26th, 2012, 03:01 PM   #2
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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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