If the roots of the equation x³ - 15x² + 71x - k = 0 are in A.P, then k is equal to

Let the roots of the cubic equation in arithmetic progression be a - d, a, and a + d. The sum of the roots gives (a - d) + a + (a + d) = 15, which simplifies to 3a = 15, so a = 5. The roots are 5 - d, 5, and 5 + d, and since 5 is a root of the equation, we substitute x = 5 to get 53 - 15(52) + 71(5) - k = 0. This simplifies to 125 - 375 + 355 - k = 0, resulting in 105 - k = 0, so k equals 105.

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