Q56 / 160 · TS EAMCET 2004 · Mathematics

If the roots of the equation $4 x^3-12 x^2+11 x+k=0$ are in arithmetic progression, then $k$ is equal to

  • Correct answer
    A
    $-3$
  • B
    $1$
  • C
    $2$
  • D
    $3$

Solution

Since, the roots of the equation $4 x^3-12 x^2$ $+11 x+k=0$ are in A.P is $\alpha-a, \alpha, \alpha+a$ $\therefore$ Sum of roots, $\quad 3 \alpha=\frac{12}{4}=3$ $$ \Rightarrow \quad \alpha=1 $$ Since, $\alpha$ is a root, therefore it satisfies the given equation $$ \Rightarrow \quad 4-12+11+k=0 \Rightarrow k=-3 \text {. } $$

Hence, the correct answer is option: 'A'.

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