Q206 / 270 · NDA 2021 (Phase 2) · Mathematics

Consider all the real roots of the equation $x^4-10 x^2+9=0$. What is the sum of the absolute values of the roots?

  • A
    4
  • B
    6
  • Correct answer
    C
    8
  • D
    10

Solution

$\begin{aligned} & x^4-10 x^2+9=0 \\ & \Rightarrow x^4-9 x^2-x^2+9=0 \\ & \Rightarrow x^2\left(x^2-9\right)-1\left(x^2-9\right)=0 \\ & \Rightarrow\left(x^2-9\right)\left(x^2-1\right)=0 \\ & \Rightarrow x^2-9=0 \text { or } x^2-1=0 \\ & \Rightarrow x= \pm 3 \text { or } x= \pm 1 \end{aligned}$ Sum of the absolute values of the roots $=3+(-3)+1+(-1)=8$

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

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