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If α and β are the zeroes of a polynomial such that α + β = -6 and αβ = 5, then the polynomial is
- a)x2 + 6x + 5 = 0
- b)x2 + 6x - 5 = 0
- c)x2 - 6x + 5 = 0
- d)x2 - 6x - 5 = 0
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If α and β are the zeroes of a polynomial such that α...
Quadratic polynomial is x2 – Sx + P = 0, where S is the sum and P is the product
⇒ x2 – (-6)x + 5 = 0
⇒ x2 + 6x + 5 = 0
Most Upvoted Answer
If α and β are the zeroes of a polynomial such that α...
Quadratic polynomial is x2 – Sx + P = 0, where S is the sum and P is the product
⇒ x2 – (-6)x + 5 = 0
⇒ x2 + 6x + 5 = 0
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If α and β are the zeroes of a polynomial such that α...
Given Information:
- The sum of the zeroes of the polynomial is -6.
- The product of the zeroes of the polynomial is 5.
Using the Sum and Product of Zeroes Formula:
- Let the polynomial be ax^2 + bx + c = 0.
- According to the given information, α + β = -b/a = -6 and αβ = c/a = 5.
- From the first equation, we have b = -6a.
- Substituting this into the second equation, we get -6a * c/a = -6c/a = 5.
- Solving for c, we get c = -5a.
Forming the Polynomial:
- Now, we have a = 1 (as the coefficient of x^2 is 1).
- Substituting a = 1 in b = -6a and c = -5a, we get b = -6 and c = -5.
- Therefore, the polynomial is x^2 - 6x - 5 = 0.
Conclusion:
- The polynomial with zeroes satisfying the given conditions is x^2 - 6x - 5 = 0, which is option 'A'.
- The sum of the zeroes of the polynomial is -6.
- The product of the zeroes of the polynomial is 5.
Using the Sum and Product of Zeroes Formula:
- Let the polynomial be ax^2 + bx + c = 0.
- According to the given information, α + β = -b/a = -6 and αβ = c/a = 5.
- From the first equation, we have b = -6a.
- Substituting this into the second equation, we get -6a * c/a = -6c/a = 5.
- Solving for c, we get c = -5a.
Forming the Polynomial:
- Now, we have a = 1 (as the coefficient of x^2 is 1).
- Substituting a = 1 in b = -6a and c = -5a, we get b = -6 and c = -5.
- Therefore, the polynomial is x^2 - 6x - 5 = 0.
Conclusion:
- The polynomial with zeroes satisfying the given conditions is x^2 - 6x - 5 = 0, which is option 'A'.
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If α and β are the zeroes of a polynomial such that α + β = -6 and αβ = 5, then the polynomial isa)x2 + 6x + 5 = 0b)x2 + 6x - 5 = 0c)x2 - 6x + 5 = 0d)x2 - 6x - 5 = 0Correct answer is option 'A'. Can you explain this answer?
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If α and β are the zeroes of a polynomial such that α + β = -6 and αβ = 5, then the polynomial isa)x2 + 6x + 5 = 0b)x2 + 6x - 5 = 0c)x2 - 6x + 5 = 0d)x2 - 6x - 5 = 0Correct answer is option 'A'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about If α and β are the zeroes of a polynomial such that α + β = -6 and αβ = 5, then the polynomial isa)x2 + 6x + 5 = 0b)x2 + 6x - 5 = 0c)x2 - 6x + 5 = 0d)x2 - 6x - 5 = 0Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If α and β are the zeroes of a polynomial such that α + β = -6 and αβ = 5, then the polynomial isa)x2 + 6x + 5 = 0b)x2 + 6x - 5 = 0c)x2 - 6x + 5 = 0d)x2 - 6x - 5 = 0Correct answer is option 'A'. Can you explain this answer?.
If α and β are the zeroes of a polynomial such that α + β = -6 and αβ = 5, then the polynomial isa)x2 + 6x + 5 = 0b)x2 + 6x - 5 = 0c)x2 - 6x + 5 = 0d)x2 - 6x - 5 = 0Correct answer is option 'A'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about If α and β are the zeroes of a polynomial such that α + β = -6 and αβ = 5, then the polynomial isa)x2 + 6x + 5 = 0b)x2 + 6x - 5 = 0c)x2 - 6x + 5 = 0d)x2 - 6x - 5 = 0Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If α and β are the zeroes of a polynomial such that α + β = -6 and αβ = 5, then the polynomial isa)x2 + 6x + 5 = 0b)x2 + 6x - 5 = 0c)x2 - 6x + 5 = 0d)x2 - 6x - 5 = 0Correct answer is option 'A'. Can you explain this answer?.
Solutions for If α and β are the zeroes of a polynomial such that α + β = -6 and αβ = 5, then the polynomial isa)x2 + 6x + 5 = 0b)x2 + 6x - 5 = 0c)x2 - 6x + 5 = 0d)x2 - 6x - 5 = 0Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for ACT.
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If α and β are the zeroes of a polynomial such that α + β = -6 and αβ = 5, then the polynomial isa)x2 + 6x + 5 = 0b)x2 + 6x - 5 = 0c)x2 - 6x + 5 = 0d)x2 - 6x - 5 = 0Correct answer is option 'A'. Can you explain this answer?, a detailed solution for If α and β are the zeroes of a polynomial such that α + β = -6 and αβ = 5, then the polynomial isa)x2 + 6x + 5 = 0b)x2 + 6x - 5 = 0c)x2 - 6x + 5 = 0d)x2 - 6x - 5 = 0Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of If α and β are the zeroes of a polynomial such that α + β = -6 and αβ = 5, then the polynomial isa)x2 + 6x + 5 = 0b)x2 + 6x - 5 = 0c)x2 - 6x + 5 = 0d)x2 - 6x - 5 = 0Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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