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If α and β are the roots of the equation 2x2 – 7x + 8 = 0, then the equation whose roots are(3α – 4β) and (3β – 4α) is _______.
  • a)
    2x2 + 7x + 98 = 0
  • b)
    x2 + 7x + 98 = 0
  • c)
    2x2 – 7x – 98 = 0
  • d)
    2x2 – 7x + 98 = 0
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If α and β are the roots of the equation 2x2 – 7x + 8...
2x2 – 7x + 8 = 0
α, β are roots of above equation (ax2 + bx + c = 0)
∴ α + β = −b/a​ = 7/2 -(1)
αβ = 8/2​(c/a​) = 4
Roots of other eqn ⇒ (3α − 4β), (3β − 4α)
⇒ sum of roots = 3α − 4β + 3β − 4α
= −α − β = −(α + β)
=(−7/2​) (from (1))
⇒ product of roots ⇒ (3α − 4β)(3β − 4α)
= 9αβ − 12α2 − 12β2 + 16αβ
= 25αβ − 12(α2 + β2)
= 25αβ − 12((α + β)2 − 2αβ)
= 25αβ − 12(α + β)2 + 21αβ
= 49αβ − 12(α + β)2
⇒ 49(4) − 12(7​/2)2
⇒ 49(4) − 12 × 49/4 ​= 49(4 − 3)
⇒ (49)
⇒ quadratic poly ⇒ x2 - (sum of roots)x +(product of roots)
⇒ x2 − (2 − 7​)x + 49
⇒ 2x2 + 7x + 98
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If α and β are the roots of the equation 2x2 – 7x + 8...
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If α and β are the roots of the equation 2x2 – 7x + 8 = 0, then the equation whose roots are(3α – 4β) and (3β – 4α) is _______.a)2x2 + 7x + 98 = 0b)x2 + 7x + 98 = 0c)2x2 – 7x – 98 = 0d)2x2 – 7x + 98 = 0Correct answer is option 'A'. Can you explain this answer?
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If α and β are the roots of the equation 2x2 – 7x + 8 = 0, then the equation whose roots are(3α – 4β) and (3β – 4α) is _______.a)2x2 + 7x + 98 = 0b)x2 + 7x + 98 = 0c)2x2 – 7x – 98 = 0d)2x2 – 7x + 98 = 0Correct answer is option 'A'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If α and β are the roots of the equation 2x2 – 7x + 8 = 0, then the equation whose roots are(3α – 4β) and (3β – 4α) is _______.a)2x2 + 7x + 98 = 0b)x2 + 7x + 98 = 0c)2x2 – 7x – 98 = 0d)2x2 – 7x + 98 = 0Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If α and β are the roots of the equation 2x2 – 7x + 8 = 0, then the equation whose roots are(3α – 4β) and (3β – 4α) is _______.a)2x2 + 7x + 98 = 0b)x2 + 7x + 98 = 0c)2x2 – 7x – 98 = 0d)2x2 – 7x + 98 = 0Correct answer is option 'A'. Can you explain this answer?.
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