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Question
State which of the following statement is true and which is false. Justify your answer.
3 ∉ {x | x4 – 5x3 + 2x2 – 112x + 6 = 0}
Options
True
False
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Solution
This statement is True.
Explanation:
Given that: 3 ∉ {x | x4 – 5x3 + 2x2 – 112x + 6 = 0}
∴ x4 – 5x3 + 2x2 – 112x + 6 = 0
Now for x = 3, we have
(3)4 – 5(3)3 + 2(3)2 – 112(3) + 6
⇒ 81 – 135 + 18 – 336 + 6
⇒ – 366 ≠ 0
Hence, This statement is True.
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