# A quesion on establishment of nature of roots

1. May 20, 2012

### Akshay_Anti

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. May 20, 2012

### Infinitum

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

3. May 20, 2012

### Akshay_Anti

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?

4. May 20, 2012

### Number Nine

The link Infinitum posted outlines the procedure. The rational zero theorem clearly describes all possible rational roots of the equation.