Q61.The value of λ such that sum of the squares of the roots of the quadratic equation, x2 + (3 −λ) x + 2 = λ has the least value is: (1) 2 (2) 49 (3) 15 (4) 1 8
What This Question Tests
This question tests the application of Vieta's formulas to express the sum of squares of roots in terms of the coefficients and then finding the minimum value of the resulting quadratic expression using calculus or properties of parabolas.
Concepts Tested
Formulas Used
α+β = -b/a
αβ = c/a
α² + β² = (α+β)² - 2αβ
λ = -b/(2a) for minimum of aλ²+bλ+c
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📋 Question Details
- Chapter
- Quadratic Equations
- Topic
- Roots of a quadratic equation
- Year
- 2019
- Shift
- 10 Jan Shift 2
- Q Number
- Q61
- Type
- MCQ
- NCERT Ref
- Class 10 Mathematics Ch 4: Quadratic Equations
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