Let a, b and c be non-zero real numbers such that b2 < 4ac, and f(x) = ax2 + bx + c. If the set S consists of all integers m such that f(m) < 0, then the set S must necessarily be
Explanation:
Since b2 < 4ac ⇒ D < 0, hence, the roots of f(x) are imaginary.
Case 1: a > 0 Since a > 0 and D < 0 ⇒ f(x) > 0 Hence, there is no value of m for which f(m) < 0 ⇒ m is an empty set.
Case 2: a < 0 Since a < 0 and D < 0 ⇒ f(x) < 0 Hence, for all values of m, f(m) < 0 ⇒ m can take any integral value.
Hence, option (c).
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