NIMCET 2017 Question Paper with solutions

Question : 82 of 120

Marks: +1, -0

The equation

(x-a)^3+(x-b)^3+(x-c)^3

has

Solution:

Let
f (x) =

(x-a)^3+(x-b)^3+(x-c)^3

∴ f'(x) =

3(x-a)^3+3(x-b)^3+3(x-c)^3

= 3 [

(x-a)^2+(x-b)^2+(x-c)^2

]
∴ f'(x) > 0 x ∊ R
∴ f ' (x) = 0 has no real roots.
Hence, f(x) = 0 has two imaginary and one real root.

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