What is the number of real roots of the polynomial
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The number of distinct real roots of the equation
$x^9+x^7+x^5+x^3+x+1=0.$
polynomials
asked 2012-08-23
user id:38512
24
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no Sir....But I want to solve it without using graph. – 2012-08-23
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$$1+x+x^3+x^5+x^7+x^9=\left(\frac{x^{10}-1}{x^2-1}\right)x+1$$ might be helpful... – 2012-08-23
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I ask about whether you know anything about the graph, because this is the way I grew my knowledge of how functions work. There is some sophisticated machinery for finding the number of roots in a general case. Here you are adding simple powers of $x$ - and, for example, $x^9$ is an increasing function. What happens when you add increasing functions together? – 2012-08-23
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plotting this will indicate -0.620374 is the root if you need it for practical purposes. – 2012-08-23