This is a Test of Mathematics Solution Subjective 70 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance.

Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta

## 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.