Q159 / 270 · NDA 2015 (Phase 2) · Mathematics

The number of real roots of the equation $x^2-3|x|+2=0$ is

  • Correct answer
    A
    4
  • B
    3
  • C
    2
  • D
    1

Solution

$\mathrm{x}^2-3|\mathrm{x}|+2=0$ Case (i) when $x \geq 0$ $\begin{aligned} & x^2-3 x+2=0 \\ & (x-1)(x-2)=0 \end{aligned}$ $x=1,2$ (both roots satisfy the condition $x \geq 0)$ Case (ii) when $\mathrm{x} \lt 0$ $\begin{aligned} & x^2+3 x+2=0 \\ & (x+1)(x+2)=0 \\ & x=-1,-2(\text { both roots satisfy the condition } x \lt 0) \end{aligned}$ So no. of real roots is 4 .

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

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