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If the roots of the equation 16 x^3-44 x^2+36 x-9=0 are in harmonic progression, then its greatest root is

Options

A3 4
B3 2
C1 2
D- 1 2

Correct answer

B. 3 2

Step-by-step solution

The given equation is 16 x^3-44 x^2+36 x-9=0 Let , and are in H.P. 3 = 1 + 1 + 1 3 = + + 3 = 36 / 16 9 / 16 =4 = 3 4 Now, + + = 11 4 + = 11 4 - 3 4 =2 ...(i) And = 9 16 = 9 16 4 3 = 3 4 ...(ii) Solving eqn. (i) and (ii) : = 3 2 , = 1 2 Greatest root is = 3 2 .

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