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Given that a, g are roots of the equation, Ax2–4x+1 = 0 and β, δ the roots of the equation, Bx2 – 6x + 1 = 0, find values of A and B, such that α, β, ŷ & δ are in H.P.
 [REE 2000, 5]
  • a)
    3,8
  • b)
    4,8
  • c)
    3,6
  • d)
    5,6
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Given that a, g are roots of the equation, Ax2–4x+1 = 0 and &bet...
As, a, g are the roots of the equation Ax^2 – 4x + 1 = 0, so 
a + g  = 4/A         (i)
and ag = 1/A       (ii)

Given, b, d are the roots of the equation Bx^2 – 6x + 1 = 0, so 
b + d = 6/B        (iii) 
and bd = 1/B      (iv) 

Given, 
a, b, g, d
 are in H.P., so 
Also b is the root of the equation Bx2 – 6x + 1 = 0, so 
Bb^2 - 6b + 1 = 0 
⇒ B x (1/4) - 6 x (1/2) + 1 = 0 
⇒ (B/4) - 2 = 0 
⇒ (B/4) = 2 
⇒ B = 8 

Given, γ is the root of the equation Ax2 – 4x + 1 = 0, so 
Ag^2 - 4g + 1 = 0 
⇒ A x (1/9) - 4 x (1/3) + 1 = 0 
⇒ (A/9) - (1/3) = 0 
⇒ A = 3. 

A, B = 3, 8 respectively.
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Given that a, g are roots of the equation, Ax2–4x+1 = 0 and β, δ the roots of the equation, Bx2 – 6x + 1 = 0, find values of A and B, such that α, β, ŷ & δ are in H.P.[REE 2000, 5]a)3,8b)4,8c)3,6d)5,6Correct answer is option 'A'. Can you explain this answer?
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Given that a, g are roots of the equation, Ax2–4x+1 = 0 and β, δ the roots of the equation, Bx2 – 6x + 1 = 0, find values of A and B, such that α, β, ŷ & δ are in H.P.[REE 2000, 5]a)3,8b)4,8c)3,6d)5,6Correct 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 Given that a, g are roots of the equation, Ax2–4x+1 = 0 and β, δ the roots of the equation, Bx2 – 6x + 1 = 0, find values of A and B, such that α, β, ŷ & δ are in H.P.[REE 2000, 5]a)3,8b)4,8c)3,6d)5,6Correct 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 Given that a, g are roots of the equation, Ax2–4x+1 = 0 and β, δ the roots of the equation, Bx2 – 6x + 1 = 0, find values of A and B, such that α, β, ŷ & δ are in H.P.[REE 2000, 5]a)3,8b)4,8c)3,6d)5,6Correct answer is option 'A'. Can you explain this answer?.
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