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
Suppose that all roots of the polynomial equation
= 0 are positive real numbers.
Show that all the roots of the polynomial are equal.
= 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.
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
Suppose that all roots of the polynomial equation
= 0 are positive real numbers.
Show that all the roots of the polynomial are equal.
= 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.