CAT 2019 Inequalities Question (Medium)

Question

Consider the function f x x 4 x 6 x 8 cdots x 98 . The number of integers x for which f x 0 is

Optima Learn · Accepted Answer

The factors are , x 4 , x 6 , x 8 , ldots, x 98 ,. So the roots are x -4,-6,-8, ldots,-98. This is an arithmetic progression from -4 to -98 with common difference -2, so the number of roots factors is 2 1 2 1 47 1 48. For x -4, every factor x k 0, so f x 0. Between two consecutive roots, the sign of

CAT 2019 Inequalities — Previous Year Question

CAT 2019

Quantitative

Inequalities

Medium

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