The value of λ such that sum of the squares of the roots of the quadratic equation, x2 + (3

Engineering

Mathematics

Quadratic Equation and Nature of Roots

Question

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

$\frac{4}{9}$

$\frac{15}{8}$

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α² + β² = (α + β)² – 2αβ

= (3 – λ)² – 2 (2 – λ)

= λ² + 9 – 6λ – 4 + 2λ

= λ² – 4λ + 5

$∴$ For least value λ = 2