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Question

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



A

(0,1)

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B

(,1]

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C

[1,)

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D

(,)

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Solution

The correct option is B

(,)


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<.


Mathematics

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