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# Test of Mathematics Solution Subjective 69 - Coefficients of Polynomial  This is a Test of Mathematics Solution Subjective 69 (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 the three equations , , and  all have only positive roots. Show that .

## Solution

If possible let , , are not all equal , , all have only positive roots. So all of , , cannot be its same sign as discriminant > 0 for three equations ( , , ). Without loss of generality we can assume or as the equations are cyclic. Now we know, , , . Now there 2 possibilities either b, c both are positive or one of b, c is positive. If b, c both are positive then, [ not possible ]. If one of b, c is positive then, [ not possible ] So a, b, c have to be equal. This is a Test of Mathematics Solution Subjective 69 (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 the three equations , , and  all have only positive roots. Show that .

## Solution

If possible let , , are not all equal , , all have only positive roots. So all of , , cannot be its same sign as discriminant > 0 for three equations ( , , ). Without loss of generality we can assume or as the equations are cyclic. Now we know, , , . Now there 2 possibilities either b, c both are positive or one of b, c is positive. If b, c both are positive then, [ not possible ]. If one of b, c is positive then, [ not possible ] So a, b, c have to be equal.

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