Calculate the number of roots of $f (| x |)$ if $f (x) = (x - 2) (x + 3) (x - 4)$ :

3

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6

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0

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4

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Solution

The correct option is D $4$
$f (x) = (x - 2) (x + 3) (x - 4)$
$= (x^{2} + x - 6) (x - 4)$
$= x^{3} - 4 x^{2} + x^{2} - 4 x - 6 x + 24$
$f (x) = x^{3} - 3 x^{2} - 10 x + 24$
$f (| x |) = (| x | - 2) (| x | + 3) (| x | - 4)$
$| x | - 2 = 0$
$| x | = 2$
$x = \pm 2$
$| x | + 3 = 0$
$| x | = - 3$
Not possible
$| x | - 4 = 0$
$| x | = 4$
$x = \pm 4$
so, four possible solutions.

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