First slide

Theory of equations

Question

The roots of the equation $|x^{2} - x - 6| = x + 2$ are

Moderate

A

$- 2, 1, 4$
B

$0, 2, 4$
C

$0, 1, 4$
D

$- 2, 2, 4$

Solution

$x + 2 \geq 0 \Rightarrow x \geq - 2$
Now, $| (x + 2) (x - 3) | = x + 2$
$\begin{array}{l} | x + 2 | | x - 3 | = x + 2 \\ \Rightarrow x + 2 = 0 or | x - 3 | = 1 \\ \Rightarrow x = - 2, x = 3 \pm 1 i.e., x = - 2, 2, 4 \end{array}$

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