First slide

Introduction to real valued functions

Question

Number of integral roots of $| x - 1 | |x^{2} - 2| = 2$ is

Moderate

A

0
B

1
C

2
D

3

Solution

We have $| x - 1 | |x^{2} - 2| = 2$
Since x is an integer, we have
$| x - 1 | = 1 and |x^{2} - 2| = 2$
or $| x - 1 | = 2 and |x^{2} - 2| = 1$
$∴ x = 0, 2 and x = 0, \pm 2$
or $x = - 1, 3 and x = \pm 1$
Therefore, solutions are -1, 0,2

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