Q.

Let x = 2 be a root of the equation x2+px+q=0 and f(x)=1cosx24px+q2+8q+16(x2p)4,x2p0,x=2p
Then  limx2p+fx
Where [. ]  denotes greatest integer function, is

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a

2

b

1

c

-1

d

0

answer is B.

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Detailed Solution

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x = 2 is a root of x2+px+q=0
q+4=2p=Lx2P+1cosx24px+q2+8q+16x24px+q2+8q+162×x24px+q2+8q+162(x2p)4
=12Ltx2P+x24px+4p22(x2p)4=12×1=12Ltx2p+[f(x)]=0

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Let x = 2 be a root of the equation x2+px+q=0 and f(x)=1−cos⁡x2−4px+q2+8q+16(x−2p)4,x≠2p0,x=2pThen  limx→2p+ fxWhere [. ]  denotes greatest integer function, is