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The largest interval for whichx^(12)+x^9...

The largest interval for which`x^(12)+x^9+x^4-x+1>0` `-4

A

`-4ltx le0`

B

`0ltx lt1`

C

`-100 lt x lt100`

D

`-ooltxltoo`

Text Solution

Verified by Experts

The correct Answer is:
D
Given, `x^(12)-x^(9)+x^(4)-x+1gt0`
here, three cases arises:
Case I When `x le0impliesx^(12)gt0,-x^(9)gt0,x^(4)gt0,-xgt0`
`thereforex^(12)-x^(9)+x^(4)-x+1 gt 0,AA x le0" "...(i)`
Case II When `0 lt x le 1`
`x^(9)lt x^(4)and x lt1implies-x^(9)+x^(4)gt0and a-xgt0`
`thereforex^(12)-x^(9)+x^(4)-x+1gt0 ltx le1`
Case III When `x gt 1 implies x^(12)gtx^(9)and x^(4)gtx`
`thereforex^(12)-x^(9)+x^(4)-x+1gt0,AAxgt1" "...(iii)`
From Eqs. (i), (ii), (iii), the above equation holds for all ` x in R.`
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