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P And Q Are Roots Of Ax^2-4x+1= 0 And R And S Are Roots Of Bx^2-6x+1=0. For What Value Of A, Will P, Q, R, S Will Be In HP?

Sujoy Das

07/02/2018 2 0

Answer:

Method 1:

OA: 63/16

p, q, r, s are in HP

Put x->1/x then roots in AP

x^2 - 4x + A = 0 and

x^2 - 6x + B = 0

Let roots be a-3d, a-d, a+d, a+3d

2a - 4d = 4

2a + 4d = 6

a= 5/2; d = 1/4

A = (a-3d)(a-d) = 63/16

B = (a+d)(a+3d) = 143/16

Method 2:

(p+q)/pq = 1/p+1/q = 4

Similarly 1/r+1/s = 6., 1/p, 1/q, 1/r, 1/s in Ap. So find p, q and find A using p+q = 4/A

p, q, r, s are in HP

Put x->1/x then roots in AP.

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