KVPY SB SX Exam 2011 Question Paper

Question : 87 of 120

Marks: +1, -0

Let

f(x)=x^12-x^9+x^4-x+1

. Which of the following is true?

Solution:

f(x) = x^9 (x^3 - 1) + x (x^3 - 1) + 1

positive for x ≥ 1 or x ≤ 0

= 1 - x + x^4- x^9 + x^12

positive for x∈(0, 1)
f(x) is always positive

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