Question
Question: The roots of the equation \| x<sup>2</sup> – x – 6 \| = x + 2, are...
The roots of the equation | x2 – x – 6 | = x + 2, are
A
– 2, 1, 4
B
– 2, 2, 4
C
0, 1, 4
D
None
Answer
– 2, 2, 4
Explanation
Solution
| x2 – x – 6 | = x + 2
Case - I when x2 – x – 6 > 0
x2 – x – 6 = x + 2, x2 – 2x – 8 = 0
x2 – 4x + 2x – 8 = 0
x (x – 4) + 2 (x –4) = 0
(x – 4) (x + 2) = 0
x = 4, x = – 2 ........ (i)
Case - II
when x2 – x – 6 < 0 – ( x2 –x – 6) = x + 2
x2 – x – 6 + x + 2 = 0
̃ x2 – 4 = 0
x = ± 2 ........ (ii)
root will be – 2 , 2 , 4