Solve: $x(x-1) (x-2) (x-3) > 0$.

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Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Calculus

Question:

Solve: $x(x-1) (x-2) (x-3) > 0$.

Options:

$(−∞,0)∪(1,2)∪(3,∞)$

$(0,1)∪(2,3)$

$(−∞,0)∪(0,1)∪(1,2)∪(2,3)∪(3,∞)$

$(−∞,0)∩(1,2)∩(3,∞)$

Correct Answer:

$(−∞,0)∪(1,2)∪(3,∞)$

Explanation:

The correct answer is Option (1) → $(−∞,0)∪(1,2)∪(3,∞)$

Given $x(x-1) (x-2) (x-3) > 0$.

Mark the numbers 0, 1, 2, 3 on real line. By method of intervals, we see that given inequality is satisfied when x > 3 or 1 < x < 2 or x < 0.

∴ The solution set is $(−∞,0)∪(1,2)∪(3,∞)$.