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The smallest positive root of the equation x⁵ - 5x⁴ - 10x³ + 50x² + 9x - 45 = 0 lies in the range

1. 0 < x ≤ 2
2. 2 < x ≤ 4
3. 6 ≤ x ≤ 8
4. 10 ≤ x ≤ 100

Correct answer: 0 < x ≤ 2

Solution

The correct option is right because evaluating the polynomial at various points shows that it changes sign between 0 and 2, indicating a root exists in that interval. Specifically, the function is negative at 0 and positive at 2, confirming the presence of a root in the specified range.

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