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Let f:RrarrR be the function f(x)=(x-a(1...

Let `f:RrarrR` be the function `f(x)=(x-a_(1))(x-a_(2))+(x-a_(2))(x-a_(3))+(x-a_(3))(x-a_(1))` with `a_(1),a_(2),a_(3) in R`. The fix `f(x)ge0` if and only if -

A

At least two of `a_(1),a_(2),a_(3)` are equal

B

`a_(1)=a_(2)=a_(3)`

C

`a_(1),a_(2),a_(3)` are all distinct

D

`a_(1), a_(2),a_(3)`, are all positive and distinct

Text Solution

Verified by Experts

The correct Answer is:
B
Only when `a_(1)=a_(2)=a_(3)`
In other cases f(x) will take both positive and negative values
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