CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Find the range of x for the following expression:

x23x+2x2+3x+21


  1. (0,81)
     

  2. None of these

  3. (,1)
     

  4. (,2)(2,1)(1,0)


Solution

The correct option is D

(,2)(2,1)(1,0)


x23x+2=(x1)(x2)and x2+3x+2=(x+1)(x+2)

For x<2:
x23x+2x2+3x+2x0
So the interval is (,2)

For 2<x<1, we obtain:
x23x+2(x2+3x+2)
2(x2+2)0
xR
So, the interval is (2,1) 

For 1<x<1, we obtain:
x23x+2x2+3x+2
3x3x
x0
So the interval is (1,0]

For 1x2, we obtain:
(x23x+2)x2+3x+2
2(x2+2)0
So, no value is possible in this interval.

For 2<x:
x23x+2x2+3x+2
3x3x
x0
So, no value is possible in this interval.

flag
 Suggest corrections
thumbs-up
 
0 Upvotes


Similar questions
View More



footer-image