CAT 2004QA Question 8

Solving InequalitiesEasy

If f(x) = x3 – 4x + p, and f(0) and f(1) are of opposite signs, then which of the following is necessarily true?

Answer & solution

  • A

    –1 < p < 2  

  • 0 < p < 3

  • C

    –2 < p < 1

  • D

    –3 < p < 0

Solution

f(x) = x3 – 4x + p

∴ f(0) = p and f(1) = p – 3

 p – 3 < p

As p and p – 3 are of opposite signs, p – 3 < 0 and p > 0.

∴ p < 3 and p > 0

∴ 0 < p < 3

Hence, option (b).

CAT 2004 QA Q8: If f(x) = x 3 &ndash; 4x + p, and f(0) and f(1) are of opposite signs, then which of the following is necessar — Solution | TheCATExam