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Real roots of equation 2x3-19x2+57x=k are first three terms of geometric progression then 1)value of k is a)216 b)108 c)-54 d)-108 2)if geometric progression is increasing sum of first n terms is(n in each option is raise to) a)(3/2)n-1 b)4((3/2)n-1) c)6((3/2)n-1) d)4(2n-1) 3if geometric progression is decreasing sum of infinite no. of terms is a)27/2 b)9 c)9/2 d)12

Real roots of equation 2x3-19x2+57x=k are first three terms of geometric progression then
1)value of k is
a)216
b)108
c)-54
d)-108

2)if geometric progression is increasing sum of first n terms is(n in each option is raise to)
a)(3/2)n-1
b)4((3/2)n-1)
c)6((3/2)n-1)
d)4(2n-1)

3if geometric progression is decreasing sum of infinite no. of terms is
a)27/2
b)9
c)9/2
d)12

Grade:11

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
6 years ago
Hello student,
Please find the answer to your question below
Given equation is 2x3-19x2+57x-k=0
Also given they are in GP so let the terms be a/r,a,ar
as the product of roots is k so k=a3
By using the formula sum of roots=a/r+a+ar=19/2
Sum of product of roots=57/2
and product of roots=k/2=a3
by solving above equations we get a=-3,
So k=-54
Similarly by applying the formula we getif geometric progression is increasing sum of first n terms is a(rn-1)/r-1=4((3/2)n-1)
Similarly by applying the formula we getif geometric progression is decreasing sum of infinite no. of terms is=a/1-r=27/2


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