Which of the following values of x do not satisfy the inequality (x2 – 3x + 2 > 0) at all?
Explanation:
If we simplify the expression x2 – 3x + 2 > 0, we get (x – 1)(x – 2) > 0. For this product to be greater than zero, either both the factors should be greater than zero or both of them should be less than zero. Therefore, (x – 1) > 0 and (x – 2) > 0 or (x – 1) < 0 and (x – 2) < 0.
Hence, x > 1 and x > 2 or x < 1 and x < 2. If we were to club the ranges, we would get either x > 2 or x < 1. So for any value of x equal to or between 1 and 2, the above equation does not follow.
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