First slide

Theory of equations

Question

The number of real roots of $| x |^{3} - 3 x^{2} + 3 | x | - 2 = 0$ is,

Moderate

A

1
B

2
C

3
D

none of these

Solution

We have
$\begin{array}{l} | x |^{3} - 3 x^{2} + 3 | x | - 2 = 0 \\ \Rightarrow | x |^{3} - 3 | x |^{2} + 3 | x | - 2 = 0 \\ \Rightarrow (| x | - 1)^{3} - 1 = 0 \\ \Rightarrow (| x | - 1)^{3} = 1 \Rightarrow | x | - 1 = 1 \Rightarrow | x | = 2 \Rightarrow x = \pm 2 . \end{array}$
Hence, there are two real roots.

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