GATE 2014 CS (CS2) – Question 15
A nonzero degree-three polynomial f has roots 1, 2 and 3. Which must be TRUE?
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Show answer and explanation
Correct answer: (A) $f(0)f(4)<0$
Explanation
Write f(x)=a(x−1)(x−2)(x−3), with a≠0. Then f(0)=−6a and f(4)=6a, whose product is−36a²<0. Therefore **A** must hold. Their sum is zero, not strictly positive or negative.