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If λ is an integer and α, β are the roots of 4x2 – 16x + λ/4 = 0 such that 1 < α < 2 and 2 < β < 3, then how many values can λ take?
  • a)
    3
  • b)
    9
  • c)
    14
  • d)
    15
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
If λ is an integer and α, β are the roots of 4x2&nda...
4x2 – 16x + λ/4 = 0
⇒ 16x2 – 64x + λ = 0
Sum of root = α + β = 64/16 = 4
Product of root = αβ = λ/16
Given 1 < α < 2 and 2 < β < 3
⇒ Value of αβ should be between 2 and 6
But we need to consider that α + β = 4
⇒ 3 < αβ < 4
Putting αβ = λ/16
⇒ 3 < λ/16 < 4
⇒ 48 < λ < 64
∴ λ can take values from 49 to 63 i.e. 15 no. of values.
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If λ is an integer and α, β are the roots of 4x2&nda...
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If λ is an integer and α, β are the roots of 4x2– 16x + λ/4 = 0 such that 1 < α < 2 and 2 < β < 3, then how many values can λ take?a)3b)9c)14d)15Correct answer is option 'D'. Can you explain this answer?
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