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Please solve it

by soumya_joy » Sat Nov 24, 2012 1:58 pm
If f(x) = x3 - 4x - p, and f(0) and f(1) are of opposite signs, then which of the following is
necessarily true?
A. - 1 < p < 2 B. 0 < p < 3 C. - 2 < p < 1 D. - 3 < p < 0
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by Anurag@Gurome » Sun Nov 25, 2012 5:01 am
soumya_joy wrote:If f(x) = x3 - 4x - p, and f(0) and f(1) are of opposite signs, then which of the following is necessarily true?
A. - 1 < p < 2 B. 0 < p < 3 C. - 2 < p < 1 D. - 3 < p < 0
f(x) = x³ - 4x - p

Hence, f(0) = -p and f(1) = -(3 + p)
Hence, p and (3 + p) are of opposite signs.

If p < 0, (3 + p) > 0 --> p > -3 --> -3 < p < 0
If p > 0, (3 + p) < 0 --> p < - 3 --> Not possible

The correct answer is D.
Anurag Mairal, Ph.D., MBA
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