The roots $\alpha ,\beta \,\,{\rm{and}}\,\gamma $ of an equation ${x^3} - 3\;a\;{x^2} + 3\;b\;x - c = 0$ are in H.P. Then,

JEE MATHEMATICS MCQ: THEORY OF EQUATION

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Analyzing +4 | -1

The roots

\alpha ,\beta \,\,\mathrm{and}\,\gamma

of an equation

{x^3} - 3\;a\;{x^2} + 3\;b\;x - c = 0

are in H.P. Then,

View answer and explanation

Correct option: D

\beta = \frac{c}{b}

Option D (

\beta = \frac{c}{b}

) is correct because the harmonic mean is the reciprocal of the arithmetic mean of the reciprocals, leading to the given relationship.

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