If x > 2 and x < 3 then which of the following is positive? 

(1) (x - 2)(x - 3) 

(II) (2 - x)(x - 3) 

(III) (2 - x)(3 - x)

Created: 5 months ago | Updated: 1 week ago
Job Solution Combined Bank (সমন্বিত ব্যাংক) সমন্বিত ১০ ব্যাংক ও আর্থিক প্রতিষ্ঠান || অফিসার (জেনারেল) (08-03-2024) গণিত
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So x is between 2 and 3.

X is more than 2, so x – 2 will be positive. X is less than 3, so x – 3 will be negative. (x – 2)(x – 3), then, is a positive times a negative, and is thus negative.

X is more than 2, so 2 – x will be negative. We already know that x – 3 is negative, so (2 – x)(x – 3) is a negative times a negative, and is thus definitely positive.

X is less than 3, so 3 – x will be positive. 2 – x is negative, so (2 – x)(3 – x) is a negative times a positive, which is negative.

We can see then, that only (2 – x)(x – 3) is positive.

5 months ago
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