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12 May 2024, 02:14
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B
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If \(x\) is an integer and \(2x^2+9 < 9x\), how many positive factors does \(x\) have?
A. 1
B. 2
C. 3
D. 4
E. 5
A. 1
B. 2
C. 3
D. 4
E. 5
12 May 2024, 02:14
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Official Solution:
If \(x\) is an integer and \(2x^2+9 < 9x\), how many positive factors does \(x\) have?
A. 1
B. 2
C. 3
D. 4
E. 5
First, rearrange the inequality: \(2x^2 - 9x + 9 < 0\). Now, factor the quadratic: \((2x - 3)(x - 3) < 0\). The roots are \(\frac{3}{2}\) and 3. Since the inequality sign is "\( < \)", the solution lies between the roots: \(1.5 < x < 3\). The only integer in this range is 2, so \(x=2\), which has two positive factors 1 and 2.
Answer: B
If \(x\) is an integer and \(2x^2+9 < 9x\), how many positive factors does \(x\) have?
A. 1
B. 2
C. 3
D. 4
E. 5
First, rearrange the inequality: \(2x^2 - 9x + 9 < 0\). Now, factor the quadratic: \((2x - 3)(x - 3) < 0\). The roots are \(\frac{3}{2}\) and 3. Since the inequality sign is "\( < \)", the solution lies between the roots: \(1.5 < x < 3\). The only integer in this range is 2, so \(x=2\), which has two positive factors 1 and 2.
Answer: B
10 Nov 2024, 01:25
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I think this is a poor-quality question and I don't agree with the explanation. Can anyone explain this? x <1.5 and x<3. And x is a positive integer which means 0<x<3 and the only value integer satisfying this is x=1 so it should be A?
