First slide

Functions (XII)

Question

The equation $| | x - 2 | + a | = 4$ can have four distinct real solutions for x if a belongs to the interval

Moderate

A

$(- \infty, - 4)$
B

$(- \infty, 0]$
C

$[4, \infty)$
D

none of these

Solution

$\begin{array}{l} |x - 2| + a = \pm 4 \\ or |x - 2| = \pm 4 - a \\ For four real roots, \\ 4 - a > 0 and - 4 - a > 0 \\ or a \in (- \infty, - 4) \end{array}$

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