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If α, β are the roots of the quadratic equation x2+ax+b=0, (b≠0); then the quadratic equation whose roots are α - 1/β, β - 1/α
  • a)
    ax2+a(b–1)x+(a–1)2=0
  • b)
    bx2+a(b–1)x+(b–1)2=0
  • c)
    x2+ax+b = 0
  • d)
    abx2+bx+a = 0
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If α, β are the roots of the quadratic equation x2+ax+b=0, ...
α+β = –a,   αβ = b
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If α, β are the roots of the quadratic equation x2+ax+b=0, ...
Understanding the Roots of the Quadratic Equation
Given the quadratic equation:
- x^2 + ax + b = 0
Let the roots be α and β.
Roots and Their Properties
Using Vieta's formulas:
- α + β = -a
- αβ = b (where b ≠ 0)
New Roots Formation
We need to find the new roots:
- α - 1/β
- β - 1/α
Finding the New Roots
1. Sum of New Roots:
- (α - 1/β) + (β - 1/α)
- = (α + β) - (1/β + 1/α)
- = (-a) - (α + β)/(αβ)
- = -a - (-a/b)
- = -a + a/b
- = a(b - 1)/b
2. Product of New Roots:
- (α - 1/β)(β - 1/α)
- = αβ - (α/αβ + β/αβ) + (1/αβ)
- = b - (α + β)/b + 1/b
- = b + a/b - 1/b
- = (b^2 + a - 1)/b
Constructing the New Quadratic Equation
Using the sum and product of new roots, we can form the new quadratic equation:
- x^2 - (sum of roots)x + (product of roots) = 0
- x^2 - (a(b - 1)/b)x + ((b^2 + a - 1)/b) = 0
Multiplying through by b gives:
- bx^2 + a(b - 1)x + (b^2 + a - 1) = 0
By comparing coefficients, we find that:
- The new quadratic equation is: bx^2 + a(b - 1)x + (b - 1)^2 = 0
Thus, the correct answer is option B.
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If α, β are the roots of the quadratic equation x2+ax+b=0, (b≠0); then the quadratic equation whose roots areα - 1/β,β - 1/αa)ax2+a(b–1)x+(a–1)2=0b)bx2+a(b–1)x+(b–1)2=0c)x2+ax+b = 0d)abx2+bx+a = 0Correct answer is option 'B'. Can you explain this answer?
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If α, β are the roots of the quadratic equation x2+ax+b=0, (b≠0); then the quadratic equation whose roots areα - 1/β,β - 1/αa)ax2+a(b–1)x+(a–1)2=0b)bx2+a(b–1)x+(b–1)2=0c)x2+ax+b = 0d)abx2+bx+a = 0Correct answer is option 'B'. 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 If α, β are the roots of the quadratic equation x2+ax+b=0, (b≠0); then the quadratic equation whose roots areα - 1/β,β - 1/αa)ax2+a(b–1)x+(a–1)2=0b)bx2+a(b–1)x+(b–1)2=0c)x2+ax+b = 0d)abx2+bx+a = 0Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If α, β are the roots of the quadratic equation x2+ax+b=0, (b≠0); then the quadratic equation whose roots areα - 1/β,β - 1/αa)ax2+a(b–1)x+(a–1)2=0b)bx2+a(b–1)x+(b–1)2=0c)x2+ax+b = 0d)abx2+bx+a = 0Correct answer is option 'B'. Can you explain this answer?.
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