Let α 1 , β 1 are the roots of x 2 –6x + p = 0 and α 2 , β 2 are the roots of x 2 –54 x + q = 0. If…

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Let α 1 , β 1 are the roots of x 2 –6x + p = 0 and α 2 , β 2 are the roots of x 2 –54 x + q = 0. If α 1 , β 1 , α 2 , β 2 form an increasing G.P., then the value of (q –p) is-

CGP EDU Academic Team · Accepted Answer

The correct answer is B. Let α 1 = a, β 1 = ar, α 2 = ar 2 , β 2 = ar 3
a + ar = 6 …(1)
ar 2 + ar 3 = 54 … (2)
Solving (1) and (2); r = 3 and a = 
q – p = a 2 r 5 – a 2 r
= a 2 r (r 4 –1)
=  × 3(81 –1) = 540
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