GATE CS 2014 Set 2 — Question 15
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Engineering Mathematics → Calculus
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Question
A non-zero polynomial of degree 3 has roots at and . Which one of the following must be TRUE?
Correct answer
(A) f(0)f(4) < 0
Solution
Since is a polynomial of degree 3 with roots at , it can be written as:where is a non-zero constant.Calculate :Calculate :Now consider the product :Since is non-zero, is always positive. Therefore, is always negative.Thus, option (A) is correct.
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