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$The largest interval for which x^{12} - x^{9} + x^{4} - x + 1 > 0 is$

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By Expert Faculty of Sri Chaitanya

a

−4

b

0

c

−100

d

−∞

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detailed solution

Correct option is D

Given expression x12−x9+x4−x+1=f(x) for x<0 put x=−y where y>0then we get f(−y)=y12+y9+y4+y+1>0 for y>0 For 00 Also 1−x>0 and x12>0⇒ x12−x9+x4+1−x>0⇒f(x)>0 For x>1,f(x)=xx3−1x8+1+1>0 Also x=0 and x=1 satisfy the inequality. So f(x)>0 for −∞

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