Q57 / 160 · TS EAMCET 2023 (13 May Shift 2) · Mathematics

If $\alpha$ is a multiple root of the equation $x^5-6 x^4+11 x^3-$ $2 x^2-12 x+8=0$ then $3 \alpha^2-2 \alpha+1=$

  • A
    -2
  • B
    1
  • C
    0
  • Correct answer
    D
    9

Solution

$x^5-6 x^4+11 x^3-2 x^2-12 x+8=0$ By observation, $x= \pm 1$ is a root $$ \begin{aligned} \therefore \quad & x^5-6 x^4+11 x^3-2 x^2-12 x+8 \\ & =(x+1)(x-1)\left(x^3-6 x^2+12 x-8\right) \\ & =(x+1)(x-1)(x-2)^3 \\ \therefore \quad & \alpha=2 \\ \Rightarrow & 3 \alpha^2-2 \alpha+1=3(2)^2-2(2)+1=9 . \end{aligned} $$

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

Relevant Questions