The value of λ, for which the sum of squares of the roots of the equation x2−(λ+2)x−λ+1=0  assumes the least value, is

The given equation is x2−(λ+2)x−λ+1=0 If the roots of the given equation are α,β  Then  Sum of the roots : α+β=λ+2  and Product of the roots : αβ=1−λ by the given condition the sum of squares of the rootsHence, α2+β2=  (α+β)2−2αβ                               =  (λ+2)2−2  (1−λ)                                =  λ2+4λ+4−2+2λ                                =  λ2+6λ+9−7                                =  (λ+3)2−7 Clearly, α2+β2 is least value when λ+3=0  i.e. When λ=−3.