Try this problem from I.S.I. B.Stat Entrance Objective Problem based on Set of real numbers.
The set of all real numbers x satisfying the inequality \(x^{3}(x+1)(x-2) \geq 0\) can be written as
Equation
Roots
Algebra
Answer:none of these
B.Stat Objective Problem 714
Challenges and Thrills of Pre-College Mathematics by University Press
\(x^{3}(x+1)(x-2) \geq 0\)
case I \(x^{3}(x+1)(x-2) \geq 0\)
or, \(0 \leq x, -1 \leq x, 2 \leq x\) which is first inequation
case II \(x^{3} \geq 0, (x+1) \leq 0, (x-2) \leq 0\)
or, \(x \geq 0, x \leq -1, x \leq 2\) which is second equation
case III \(x^{3} \leq 0, (x+1) \leq 0, (x-2) \geq 0\)
or, \(x \leq 0 x \leq -1, 2 \leq x\) which is third equation
case IV \(x^{3} \leq 0, (x+1) \geq 0, (x-2) \leq 0\)
or, \(x \leq0, x \geq -1, x \leq 2\) which is fourth equation
Combining we get \(x^{3}(x+1)(x-2) \geq 0\) satisfy if \(x\in\) \([-1,0] \bigcup [2,infinity)\)
or, answer option none of these
I.S.I. & C.M.I. Entrance Program
Taught by students and alumni of I.S.I. & C.M.I.
In 2025, 8 students from Cheenta Academy cracked the prestigious Regional Math Olympiad. In this post, we will share some of their success stories and learning strategies. The Regional Mathematics Olympiad (RMO) and the Indian National Mathematics Olympiad (INMO) are two most important mathematics contests in India.These two contests are for the students who are […]
Cheenta Academy proudly celebrates the success of 27 current and former students who qualified for the Indian Olympiad Qualifier in Mathematics (IOQM) 2025, advancing to the next stage — RMO. This accomplishment highlights their perseverance and Cheenta’s ongoing mission to nurture mathematical excellence and research-oriented learning.
Cheenta students shine at the Purple Comet Math Meet 2025 organized by Titu Andreescu and Jonathan Kanewith top national and global ranks.
Celebrate the success of Cheenta students in the Stanford Math Tournament. The Unified Vectors team achieved Top 20 in the Team Round.