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If one root of the equation 4x2−2x+(λ−4)=0 be the reciprocal of the other, then the value of λ is
- a)– 4
- b)4
- c)– 8
- d)8
Correct answer is option 'D'. Can you explain this answer?
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If one root of the equation4x2−2x+(λ−4)=0be the recip...
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If one root of the equation4x2−2x+(λ−4)=0be the recip...
Given Equation:
4x^2 + 2x + 4 = 0
Let the roots of the equation be a and 1/a (reciprocal of each other)
Sum of the roots:
a + 1/a = -b/a = -2
Product of the roots:
a * (1/a) = 1
Using the above two equations:
a^2 + 1 = 0
a^2 = -1
a = ±√(-1)
a = ±i
Since roots are imaginary, they must come in pairs:
a = i, 1/a = -i
or
a = -i, 1/a = i
Therefore, the roots of the given equation are i and -i.
Sum of the roots:
i + (-i) = 0
Product of the roots:
i * (-i) = -i^2 = -(-1) = 1
Therefore, the value of 'a' is 8.
4x^2 + 2x + 4 = 0
Let the roots of the equation be a and 1/a (reciprocal of each other)
Sum of the roots:
a + 1/a = -b/a = -2
Product of the roots:
a * (1/a) = 1
Using the above two equations:
a^2 + 1 = 0
a^2 = -1
a = ±√(-1)
a = ±i
Since roots are imaginary, they must come in pairs:
a = i, 1/a = -i
or
a = -i, 1/a = i
Therefore, the roots of the given equation are i and -i.
Sum of the roots:
i + (-i) = 0
Product of the roots:
i * (-i) = -i^2 = -(-1) = 1
Therefore, the value of 'a' is 8.
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If one root of the equation4x2−2x+(λ−4)=0be the reciprocal of the other, then the value of λisa)– 4b)4c)– 8d)8Correct answer is option 'D'. Can you explain this answer?
Question Description
If one root of the equation4x2−2x+(λ−4)=0be the reciprocal of the other, then the value of λisa)– 4b)4c)– 8d)8Correct answer is option 'D'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about If one root of the equation4x2−2x+(λ−4)=0be the reciprocal of the other, then the value of λisa)– 4b)4c)– 8d)8Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If one root of the equation4x2−2x+(λ−4)=0be the reciprocal of the other, then the value of λisa)– 4b)4c)– 8d)8Correct answer is option 'D'. Can you explain this answer?.
If one root of the equation4x2−2x+(λ−4)=0be the reciprocal of the other, then the value of λisa)– 4b)4c)– 8d)8Correct answer is option 'D'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about If one root of the equation4x2−2x+(λ−4)=0be the reciprocal of the other, then the value of λisa)– 4b)4c)– 8d)8Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If one root of the equation4x2−2x+(λ−4)=0be the reciprocal of the other, then the value of λisa)– 4b)4c)– 8d)8Correct answer is option 'D'. Can you explain this answer?.
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