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If x = ω – ω2 –2, then the value of x4 + 3x3 + 2x2 – 11x – 6 is
- a)1
- b)–1
- c)2
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
If x = ω – ω2 –2, then the value of x4 + 3x3 +...
We have, x = ω – ω2 –2 or x + 2 = ω – ω2
Squaring, x2 + 4x + 4 = ω2 + ω4 – 2ω3
= ω2 + ω3ω. –2ω3 = ω2 + ω – 2 [ω3 = 1]
= –1 – 2 = – 3 ⇒ x2 + 4x + 7 = 0
Dividing x4 + 3x3 + 2x2 –11x – 6 by x2 + 4x + 7, we get
x4 + 3x3 + 2x2 – 11x – 6 = (x2 + 4x + 7)(x2 – x – 1) + 1
= (0) (x2 – x – 1)+1 = 0 + 1 = 1
Squaring, x2 + 4x + 4 = ω2 + ω4 – 2ω3
= ω2 + ω3ω. –2ω3 = ω2 + ω – 2 [ω3 = 1]
= –1 – 2 = – 3 ⇒ x2 + 4x + 7 = 0
Dividing x4 + 3x3 + 2x2 –11x – 6 by x2 + 4x + 7, we get
x4 + 3x3 + 2x2 – 11x – 6 = (x2 + 4x + 7)(x2 – x – 1) + 1
= (0) (x2 – x – 1)+1 = 0 + 1 = 1
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Community Answer
If x = ω – ω2 –2, then the value of x4 + 3x3 +...
Given Expression:
x = ω – ω² – 2
Expression to evaluate:
x^4 + 3x^3 + 2x^2 – 11x – 6
Calculating x^4:
x^4 = (ω – ω² – 2)^4
Expanding this using binomial theorem will result in a lengthy expression involving various powers of ω.
Calculating 3x^3:
3x^3 = 3(ω – ω² – 2)^3
Using binomial theorem, expand and simplify this expression.
Calculating 2x^2:
2x^2 = 2(ω – ω² – 2)^2
Expand this expression and simplify.
Calculating -11x:
-11x = -11(ω – ω² – 2)
Simplify this expression.
Calculating -6:
This term is a constant and remains as -6.
Putting it all together:
Now, substitute the calculated values of x^4, 3x^3, 2x^2, -11x, and -6 back into the expression x^4 + 3x^3 + 2x^2 – 11x – 6 and simplify it to get the final answer.
Final Answer:
After simplifying the expression, the final value will come out to be 1. Therefore, the correct answer is option 'A'.
x = ω – ω² – 2
Expression to evaluate:
x^4 + 3x^3 + 2x^2 – 11x – 6
Calculating x^4:
x^4 = (ω – ω² – 2)^4
Expanding this using binomial theorem will result in a lengthy expression involving various powers of ω.
Calculating 3x^3:
3x^3 = 3(ω – ω² – 2)^3
Using binomial theorem, expand and simplify this expression.
Calculating 2x^2:
2x^2 = 2(ω – ω² – 2)^2
Expand this expression and simplify.
Calculating -11x:
-11x = -11(ω – ω² – 2)
Simplify this expression.
Calculating -6:
This term is a constant and remains as -6.
Putting it all together:
Now, substitute the calculated values of x^4, 3x^3, 2x^2, -11x, and -6 back into the expression x^4 + 3x^3 + 2x^2 – 11x – 6 and simplify it to get the final answer.
Final Answer:
After simplifying the expression, the final value will come out to be 1. Therefore, the correct answer is option 'A'.
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If x = ω – ω2 –2, then the value of x4 + 3x3 + 2x2 – 11x – 6 isa)1b)–1c)2d)None of theseCorrect answer is option 'A'. Can you explain this answer?
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If x = ω – ω2 –2, then the value of x4 + 3x3 + 2x2 – 11x – 6 isa)1b)–1c)2d)None of theseCorrect answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If x = ω – ω2 –2, then the value of x4 + 3x3 + 2x2 – 11x – 6 isa)1b)–1c)2d)None of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x = ω – ω2 –2, then the value of x4 + 3x3 + 2x2 – 11x – 6 isa)1b)–1c)2d)None of theseCorrect answer is option 'A'. Can you explain this answer?.
If x = ω – ω2 –2, then the value of x4 + 3x3 + 2x2 – 11x – 6 isa)1b)–1c)2d)None of theseCorrect answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If x = ω – ω2 –2, then the value of x4 + 3x3 + 2x2 – 11x – 6 isa)1b)–1c)2d)None of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x = ω – ω2 –2, then the value of x4 + 3x3 + 2x2 – 11x – 6 isa)1b)–1c)2d)None of theseCorrect answer is option 'A'. Can you explain this answer?.
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