Theory of Equations 1 Question 34
35. The number of real solutions of the equation $|x|^{2}-3|x|+2=0$ is
(1982, 1M)
(a) 4
(b) 1
(c) 3
(d) 2
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Solution:
- Since, $|x|^{2}-3|x|+2=0$
$$ \begin{aligned} & \Rightarrow \quad(|x|-1)(|x|-2)=0 \\ & \Rightarrow \quad|x|=1,2 \\ & \therefore \quad x=1,-1,2,-2 \end{aligned} $$
Hence, four real solutions exist.
