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Question
What is the solution set of the equation x3−x2+x−1>0?
What is the solution set of the equation x3−x2+x−1>0?
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Solution
The correct option is C x > 1
Best way to solve this problem is by simply assuming some values for x.
Put x = 2, then x3−x2+x−1=5>0, which is true.
Hence, option (a) and (b) are eliminated.
Put x = 1, then x3−x2+x−1=0 is not greater than 0, hence option (d) is eliminated.
∴ Option (c) is correct answer.
Alternative Approach:
x3−x2+x−1>0
x2(x−1)+(x−1)>0
(x2+1)(x−1)>0
As, x2+1>0 for all x, so, x > 1.
Best way to solve this problem is by simply assuming some values for x.
Put x = 2, then x3−x2+x−1=5>0, which is true.
Hence, option (a) and (b) are eliminated.
Put x = 1, then x3−x2+x−1=0 is not greater than 0, hence option (d) is eliminated.
∴ Option (c) is correct answer.
Alternative Approach:
x3−x2+x−1>0
x2(x−1)+(x−1)>0
(x2+1)(x−1)>0
As, x2+1>0 for all x, so, x > 1.
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