CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

The largest interval for which x22x19+x14x5+1>0 is


  1. (0,1)

  2. (,1]

  3. [1,)

  4. (,)


Solution

The correct option is D

(,)


If x0
x220,x140,x190,x50x22x19+x14x5+1>0

If 0<x<1, then x5<1 and hence
x22x19+x14x5+1=x22+x14(1x5)+(1x5)
So, x22x19+x14x5+1>0 when  0<x<1.

If x>1; then x3>1
x22x19+x14x5+1=x19(x31)+x5(x91)+1>0

Hence, x22x14x5+1>0 for <x<.

flag
 Suggest corrections
thumbs-up
 
0 Upvotes



footer-image