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:

α + β = λ - 3
αβ = 2 - λ
α² + β² = (α + β)² - 2αβ = (λ - 3)² - 2(2 - λ) = λ² - 6λ + 9 - 4 + 2λ = λ² - 4λ + 5 = (λ - 2)² + 1
Therefore, the least value occurs when λ = 2