Multiple choice

Three real roots of the equation $2x^{3}-19x^{2}+57x+2\lambda =0$ are consecutive term of geometrical progression, then the value $\lambda$ is

  1. $54$
  2. $-54$
  3. $-27$
  4. $-108$
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C Correct answer
Explanation

Let the roots be a/r, a, ar. Sum of roots = 19/2, product of roots = -2lambda/2 = -lambda. From the sum of roots taken two at a time: (a/r * a) + (a * ar) + (a/r * ar) = 57/2. Solving these equations for a and lambda yields lambda = -27.

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