2
$\begingroup$

The number of distinct real roots of the equation

$x^9+x^7+x^5+x^3+x+1=0.$

  • 0
    no Sir....But I want to solve it without using graph.2012-08-23
  • 0
    $$1+x+x^3+x^5+x^7+x^9=\left(\frac{x^{10}-1}{x^2-1}\right)x+1$$ might be helpful...2012-08-23
  • 1
    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
  • 0
    plotting this will indicate -0.620374 is the root if you need it for practical purposes.2012-08-23

1 Answers 1