Suppose A, B, C are defined as A = a^(2)...

Suppose A, B, C are defined as `A = a^(2)b + ab^(2) - a^(2)c - ac^(2), B = b^(2)c + bc^(2) - a^(2)b - ab^(2)`, and `C = a^(2)c + ac^(2) - b^(2)c - bc^(2)`, where `a gt b gt c gt 0` and the equation `Ax^(2) + Bx + C = 0` has equal roots, then a, b, c are in

A

A.P.

B

G.P.

C

H.P.

D

None of these

Text Solution

Verified by Experts

The correct Answer is:

C

Promotional Banner

Promotional Banner

Topper's Solved these Questions

SEQUENCE AND SERIES
VIKAS GUPTA (BLACK BOOK)|Exercise EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)|18 Videos
SEQUENCE AND SERIES
VIKAS GUPTA (BLACK BOOK)|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|17 Videos
QUADRATIC EQUATIONS
VIKAS GUPTA (BLACK BOOK)|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|45 Videos
SOLUTION OF TRIANGLES
VIKAS GUPTA (BLACK BOOK)|Exercise Exercise-5 : Subjective Type Problems|12 Videos

Similar Questions

Explore conceptually related problems

If a^(2) + b^(2) + c^(2) = 0 and |(b^(2) + c^(2) ,ab,ac),(ab,c^(2) + a^(2),bc),(ac,bc,a^(2) + b^(2))| = k a^(2) b^(2) c^(2) , then the value of k is

If a, b, c are non zero complex numbers satisfying a^(2) + b^(2) + c^(2) = 0 and |(b^(2) + c^(2),ab,ac),(ab,c^(2) + a^(2),bc),(ac,bc,a^(2) + b^(2))| = k a^(2) b^(2) c^(2) , then k is equal to

| [-bc, b ^ (2) + bc, c ^ (2) + bca ^ (2) + ac, -ac, c ^ (2) + aca ^ (2) + ab, b ^ (2) + ab, -ab (ab + bc + ac), is = 64. then

Let a, b and c be real numbers such that 4a + 2b + c = 0 and ab gt 0. Then the equation ax^(2) + bx + c = 0 has

Show that (a^(2) +ab+b^(2)) ,(c^(2) +ac +a^(2)) and ( b^(2) +bc+ c^(2)) are in AP, if a,b,c are in AP.

det[[bc-a^(2),ca-b^(2),ab-c^(2)ca-b^(2),ab-c^(2),bc-a^(2)ab-c^(2),bc-a^(2),ca-b^(2)]]=det[[a,b,cb,c,ac,a,b]]^(2)

If in a triangle ABC/_B=60^(@), then (A) (a-b)^(2)=c^(2)-ab(B)(b-c)^(2)=a^(2)-bc(C)(c-a)^(2)=b^(2)-ac(D)a^(2)+b^(2)+c^(2)=2b^(2)+ac^(2)

Suppose a,b,c gt 0 and p in R. if (a^(2)+b^(2))p^(2)-2(ab+bc)p+(b^(2)+c^(2))=0 then a,b,c are in

VIKAS GUPTA (BLACK BOOK)-SEQUENCE AND SERIES -EXERCISE (SUBJECTIVE TYPE PROBLEMS)

Suppose A, B, C are defined as A = a^(2)b + ab^(2) - a^(2)c - ac^(2), ...
Text Solution
|
Let a ,b ,c ,d be four distinct real numbers in A.P. Then half of the ...
Text Solution
|
The sum of all digits of n for which sum (r =1) ^(n ) r 2 ^(r ) = 2+2^...
Text Solution
|
If lim ( x to oo) (r +2)/(2 ^(r+1) r (r+1))=1/k, then k =
Text Solution
|
The value of sum (r =1) ^(oo) (8r)/(4r ^(4) +1) is equal to :
Text Solution
|
Three non-zero real numbers from an A.P. and the squares of these numb...
Text Solution
|
The sum of the fourth and twelfth term of an arithmetic progression is...
Text Solution
|
In an increasing sequence of four positive integers, the first 3 terms...
Text Solution
|
The limit of (1)/(n ^(4)) sum (k =1) ^(n) k (k +2) (k +4) as n to oo i...
Text Solution
|
Which is the last digit of 1+2+3+……+ n if the last digit of 1 ^(3) + ...
Text Solution
|
There distinct positive numbers, a,b,c are in G.P. while log (c) a, lo...
Text Solution
|
The numbers 1/3, 1/3 log (x) y, 1/3 log (y) z, 1/7 log (x) x are in H...
Text Solution
|
If sum ( k =1) ^(oo) (k^(2))/(3 ^(k))=p/q, where p and q are relativel...
Text Solution
|
The sum of the terms of an infinitely decreassing Geometric Progressio...
Text Solution
|
A cricketer has to score 4500 runs. Let a (n) denotes the number of ru...
Text Solution
|
If x=10 sum(r=3) ^(100) (1)/((r ^(2) -4)), then [x]= (where [.] deno...
Text Solution
|
Let f (n)=(4n + sqrt(4n ^(2) +1))/( sqrt(2n +1 )+sqrt(2n-1)),n in N th...
Text Solution
|
Find the sum of series 1+1/2+1/3+1/4+1/6+1/8+1/9+1/12+…… oo, where the...
Text Solution
|
Let a (1), a(2), a(3),…….., a(n) be real numbers in arithmatic progres...
Text Solution
|
Let the roots of the equation 24 x ^(3) -14x ^(2) + kx +3=0 form a geo...
Text Solution
|
How many ordered pair (s) satisfy log (x ^(2) + (1)/(3) y ^(3) + (1)/(...
Text Solution
|