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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.

  1. there is only one root
  2. sum of the roots is + 1
  3. sum of the roots is zero
  4. 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.

  • 6
    I think the point of the question is to notice the equation is quadratic in $ |x| $ rather than use cases.2010-10-21
  • 0
    The equation is short enough to post in the title of the question.2010-10-21
  • 0
    @T..: Corrected :)2010-10-21
  • 2
    Just to be perfectly clear: the minus sign in $-x$ doesn't mean that $-x$ is negative. It means that $-x=0-x$, so it is negative if $x$ is positive and vice versa. I had a teacher who insisted on reading $-x$ as "minus x" rather than "negative x" for this very reason.2010-10-21
  • 0
    @Paul, tortuous, but I perfectly understand your teacher's insistence. :) I have to say there are still a lot of people who have a hard time grasping "the negative of a negative is positive", both in mathematics and in language.2010-10-21
  • 0
    @J.M.: and there are waaaaay too many people that think that if there is a minus sign, then it means it's negative...2010-10-21
  • 0
    It's definitely not an uncommon situation, @Arturo. :)2010-10-21

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