Question 64

Consider the function f(x) = (x + 4)(x + 6)(x + 8) ⋯ (x + 98). The number of integers x for which f(x) < 0 is:

Solution

The critical points of the function are -4, -6, -8, ... , -98 ( 48 points).

For all integers less than -98  and greater than -4 f(x) > 0 always .

for x= -5, f(x) < 0 

Similarly, for x= -9, -13, ...., -97 (This is an AP with common difference -4)

Hence, in total there are 24 such integers satisfying f(x)< 0.

Video Solution

video

Create a FREE account and get:

  • All Quant Formulas and shortcuts PDF
  • 15 XAT previous papers with solutions PDF
  • XAT Trial Classes for FREE

    cracku

    Boost your Prep!

    Download App