If β is a root of the eqn---
zn + 2zn-1 +3zn-2+18n + 12=0 which lies inside the circle |z|<=1 . Then 3|β| >
a.2
b.1
c.3
d.0
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3 Answers
11:) :) no man.. FIIJEE MATHS HOD cudnt do it after takin abt 20 mins,,none of d gud studs i asked too..they all quite after takin 1/2 an hour,,telling they will do it some other day.. :) can u do it ??pls tell soln. if u can..
62zn + 2zn-1 +3zn-2+18n + 12=0
zn + 2zn-1 +3zn-2 = -18n - 12
For different values of n , the RHS will take values such that the minimum modulus is 6
if |Z|<=1
then LHS has a maximum value of 6
for them to be equal LHS has to be 6 and RHS has to be 6
so
zn + 2zn-1 +3zn-2 = 6
so |z2 + 2z +3| =6 which is possible when z=1
so beta is 1
so 3beta =3
which is greater than 0,1 , 2