If the roots of the equation $4 x^{3} - 12 x^{2} + 11 x + k = 0$ are in A.P. Then $k =$

- 3

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Solution

The correct option is D $- 3$
Let roots of $4 x^{3} - 12 x^{2} + 11 x + k = 0$ are $a - d, a, a + d$
Then $s_{1} = a - d + a + a + d = \frac{12}{4} \Rightarrow a = 1$
And as $a$ is also root it will satisfies equation then $k = - 3$

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