2x^3 -5x -4x +3
(X-1)(x-9)<0
(X-1)(x-9)<0
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Can you check the first question. Is the 2nd term meant to be 5x^2?
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(x-1)(x-9) < 0
For the product to be negative (ie: less that zero) one factor must be positive and the other must be negative.
When x > 9, both factors are positive, and their product is positive.
When x < 1, both factors are negative, but their product is positive.
When x = 1, the 1st factor is zero and the product is zero, which isn't LESS THAN zero.
When x = 9, the 2nd factor is zero and the product is zero, etc.
SOLUTION: 1 < x < 9
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(x-1)(x-9) < 0
For the product to be negative (ie: less that zero) one factor must be positive and the other must be negative.
When x > 9, both factors are positive, and their product is positive.
When x < 1, both factors are negative, but their product is positive.
When x = 1, the 1st factor is zero and the product is zero, which isn't LESS THAN zero.
When x = 9, the 2nd factor is zero and the product is zero, etc.
SOLUTION: 1 < x < 9
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