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
Suppose that the three equations ,
, and
–
all have only positive roots. Show that
.
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
Suppose that the three equations ,
, and
–
all have only positive roots. Show that
.
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.