Solve the inequality

• LastRide7

  3 Apr 11, 19:19

  Solve the inequality (x - 4)(x + 2)(x - 1)^2 < 0
  
  I feel that this question is quite tricky.
  

• FireIce

  3 Apr 11, 19:29

  x < -2, 1 < x < 4
• wee_ws

  3 Apr 11, 20:09

  Hi,

    You should elaborate further about your feeling, then there could be more discussion. Thanks.

  Cheers,
  Wen Shih

• Stampboy123

  7 Apr 11, 19:50

  this question

  (x-1)^2>=0

  f(x)=(x - 4)(x + 2)(x - 1)^2<0

  so  x not eq to 1

  and (x-4)(x+2)<0 => -2<x<4

  so -2<x<1 and 1<x<4

   

• wee_ws

  8 Apr 11, 02:43

  Hi,

    To be correct, the solution is -2 < x < 1 OR 1 < x < 4. Another way of expressing the solution is -2 < x < 4 AND x =/= 1. In set notation, we can write x ϵ (-2, 1) ∪ (1, 4).

    It is deceptive because there is a value in between that is not applicable. This type of question is common in school exams but rare in Cambridge questions. Thanks.

  Cheers,
  Wen Shih