KVPY SX SB Exam 2016 Question Paper

Question : 13 of 120

Marks: +1, -0

The polynomial equation

x^3 - 3ax^2 + (27a^2 + 9)x + 2016 = 0

has -

Solution:

f'(x) = 3x^2- 6ax + 27a^2 + 9

= 3[x^2- 2ax + 9a^2 + 3]

= 3((x - a)^2 + 8a^2 + 3)

∴ f'(x) is + ve for x ∈ R so f(x) is monotonic for x ∈ R.

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