f(x) = \({x^{2}+2x-15 \over {x^{2}-7x-18}}\) is negative if and only if

CAT 2021 Question Paper | CAT Verbal Ability Slot 1

Question :

Started 3 months ago by Shashank in

A.
-5 < x < -2 or 3 < x < 9
B.
-2 < x < 3 or x > 9
C.
x < -5 or 3 < x < 9
D.
x < -5 or -2 < x < 3

Option A is the correct answer.

Explanatory Answer

Keeping these roots on the number line and checking for the range where f(x) becomes negative.
For the numbers below -5, f(x) is positive.
For the numbers between -5 and -2, the value f(x) is negative.
For the numbers between -2 and 3, the value of f(x) is positive.
For the numbers between 3 and 9, the value of f(x) is negative.
For the numbers above 9, the value of f(x) is positive.
Hence the range should be -5 < x < -2 and 3 < x < 9.