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Sets — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSSets2 Marks
Question
State the following statement is true and false. Justify your answer.
$3\notin\{\text{x}|\text{x}^4-5\text{x}^3+2\text{x}^2-112\text{x}+6=0\}$
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Answer

Given that: $3\notin\{\text{x}|\text{x}^4-5\text{x}^3+2\text{x}^2-112\text{x}+6=0\}$
$\therefore\text{x}^4-5\text{x}^3+2\text{x}^2-112\text{x}+6=0$
Now for x = 3, we have
(3)4 - 5(3)3 + 2(3)2 - 112(3) + 6 = 0
⇒ 81 - 135 + 18 - 336 + 6 = 0 which is not true
So 3 cannot be an element of the given set.
Hence, statement (iii) is 'True'.

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