Answer :

Given that a and b are roots of x2 – 3x + p = 0


a + b = 3 and ab = p ...(i)


It is given that c and d are roots of x2 – 12x + q = 0


c + d = 12 and cd = q...(ii)


Also given that a, b, c, d are in G.P.


Let a, b, c, d be the first four terms of a G.P.


a = a, b = ar c = ar2 d = ar3


Now,


a + b = 3


a + ar = 3


a(1 + r) = 3…(iii)


c + d = 12


ar2 + ar3 = 12


ar2(1 + r) = 12.....(iv)


From (iii) and (iv) we get


3.r2 = 12


r2 = 4


r = ±2


Substituting the value of r in (iii) we get a = 1


b = ar = 2


c = ar2 = 22 = 4


d = ar3 = 23 = 8


ab = p = 2and cd = 4×8 = 32


q + p = 32 + 2 = 34 and q−p = 32−2 = 30


q + p:q−p = 34:30 = 17:15


Hence, proved.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

A person has 2 paRD Sharma - Mathematics

The sum of the seRD Sharma - Mathematics

How many terms ofRD Sharma - Mathematics

If <span lang="ENRD Sharma - Mathematics

Let anRD Sharma - Mathematics

Find the sum of 2RD Sharma - Mathematics

If <span lang="ENRS Aggarwal - Mathematics

Find the sum (41 RS Aggarwal - Mathematics

Find the sum (2 +RS Aggarwal - Mathematics

If<span lang="EN-RS Aggarwal - Mathematics