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If α and β are the roots of the equation x2 + x + 1 = 0, then which of the following are the roots of the equation x2 – x + 1 = 0? 
  • a)
    α7 and β13
  • b)
    α13 and β7
  • c)
    α20 and β20
  • d)
    None of these
Correct answer is option 'D'. Can you explain this answer?
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If α and β are the roots of the equation x2 + x + 1 = 0, the...
Solution:

Given equation is x2 - x + 1 = 0

Let the roots of this equation be α and β.

α + β = 1 …(1)

αβ = 1 …(2)

We are to find the roots of the equation x2 - x + 1 = 0.

Let the roots of this equation be x1 and x2.

x1 + x2 = 1 …(3)

x1x2 = 1 …(4)

Now, we can see that none of the given options have roots which satisfy both equations (1) and (2).

Therefore, none of the given options are the roots of the equation x2 - x + 1 = 0.

Hence, the correct answer is option D, None of these.
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If α and β are the roots of the equation x2 + x + 1 = 0, the...
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If α and β are the roots of the equation x2 + x + 1 = 0, then which of the following are the roots of the equation x2 – x + 1 = 0?a)α7 and β13b)α13 and β7c)α20 and β20d)None of theseCorrect answer is option 'D'. Can you explain this answer?
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If α and β are the roots of the equation x2 + x + 1 = 0, then which of the following are the roots of the equation x2 – x + 1 = 0?a)α7 and β13b)α13 and β7c)α20 and β20d)None of theseCorrect answer is option 'D'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about If α and β are the roots of the equation x2 + x + 1 = 0, then which of the following are the roots of the equation x2 – x + 1 = 0?a)α7 and β13b)α13 and β7c)α20 and β20d)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If α and β are the roots of the equation x2 + x + 1 = 0, then which of the following are the roots of the equation x2 – x + 1 = 0?a)α7 and β13b)α13 and β7c)α20 and β20d)None of theseCorrect answer is option 'D'. Can you explain this answer?.
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