Question

The roots of $|x - 2|^{2} + |x - 2| - 6 = 0$ are

• A. 0, 4
• B. –1, 3
• C. 4, 2
• D. 5, 1

Answer 1

Answer: (A)

0, 4

Answer 2

We have $|x - 2|^{2} + |x - 2| - 6 = 0$

Let $|x - 2| = X$

$X^{2} + X - 6 = 0$

⇒ $X = \frac{- 1 \pm \sqrt{1 + 24}}{2} = 2, - 3$ ⇒ $X = 2$ and $X = - 3$

∴ $|x - 2| = 2$ and $|x - 2| = - 3$, which is not possible.

⇒ $x - 2 = 2$ or $x - 2 = - 2$

∴ $x = 4$ or $x = 0$