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