This question and the described solution are copied from a test-paper :
For the equation $x^2$ + |x| - 6 = 0 analyze the four statements below for correctness.
- there is only one root
- sum of the roots is + 1
- sum of the roots is zero
- the product of the roots is +4
Answer : (3)
Answer Explanation :
If x > 0 |x| = x.
Given equation will be $x^2 + x - 6 = 0$⇒ x = 2,- 3 ⇒ x = 2
If x < 0 |x| = - x.
Given equation will b e $x^2$ - x - 6 = 0 ⇒ x = -2, 3 ⇒x = - 2
Sum of roots is 2 - 2 = 0
Now I have a doubt on the statment "If x < 0 |x| = - x." I think modulus means that |x| is always positive ?! Also I can see that (2) seems to be the correct option isn't ?!
Please post your views.