* problem*: Suppose that all roots of the polynomial equation

= 0 are positive real numbers.

Show that all the roots of the polynomial are equal.

* solution*: = 0

If the roots are , , and .

then , , and = 1

& + + + = 4.

Now all of , , and are positive so AM-GM inequality is applicable.

1 1

Now we know equality in AM-GM occours if all the numbers are equal.So , , and are all equal.