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The roots of (x-41)^(49)+(x-49)^(41)+(x-...

The roots of `(x-41)^(49)+(x-49)^(41)+(x-2009)^(2009)=0` are

A

all necessarily real

B

non-real except one positive real root

C

non-real except three positive real roots

D

non-real except for three real roots of which exactly one is positive

Text Solution

Verified by Experts

The correct Answer is:
B
We have `(x-41)^(49)+(x-49)^(41)+(x-2009)^(2009)=0`
Let `f(x)=(x-41)^(49)+(x-49)^(41)+(x-2009)^(2009)`
`therefore" "f'(x)=49(x-41)^(48)+41(x-49)^(40)+2009(x-2009)^(48)gt0`
Hence f(x) will cut x-axis only once `rArr" 1 real root"`
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