Q57 / 160 · AP EAMCET 2008 · Mathematics

The sum of the fourth powers of the roots of the equation $x^3+x+1=0$ is

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

Solution

Given equation is $x^3+x+1=0$ On comparing with $x^3+p_1 x^2+p_2 x+p_3=0$, we get Now, $$ p_1=0, p_2=1, p_3=1 $$ $$ \begin{aligned} & S_2+0 \cdot S_1+2=0 \Rightarrow S_2=-2 \\ & S_3+0 \cdot S_2+1 \cdot S_1+(2)=0 \Rightarrow S_3=-2 \\ & S_4+0 \cdot S_3+1 \cdot S_2+1 \cdot S_1=0 \\ & \Rightarrow \quad S_4+0+1(-2)+1(0)=0 \\ & S_4=2 \end{aligned} $$ $$ S_1=0, S_0=2 $$

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

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