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A quesion on establishment of nature of roots

  1. May 20, 2012 #1
    we are given an equation x5+x=10
    . How to prove that the only root for the equation is irrational? I'm an average 12th standard student. So, please keep it low. Thanks in advance.
     
  2. jcsd
  3. May 20, 2012 #2
    Did you try using the Rational root Theorem?

    It's quite clear that there is only one real root to the equation. If you can find a contradiction that the root cannot be rational, you are done :smile:
     
  4. May 20, 2012 #3
    How to contradict? Assuming a p/q form doesn't help...... the root must be of form non- terminating non-repeating decimal expansion...... how to do that?
     
  5. May 20, 2012 #4
    The link Infinitum posted outlines the procedure. The rational zero theorem clearly describes all possible rational roots of the equation.
     
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