If the equation x2+2(λ+1)x+λ2+λ+7=0 has only negative roots, then the least value of λ equals _______.

Let f(x)=x2+2(λ+1)x+λ2+λ+7If both roots of f(x) = 0 are negative, thenD=b2−4ac=4(λ+1)2−4λ2+λ+7≥0⇒ λ−6≥0⇒ λ∈[6,∞)                    ……. (1)Sum of roots = - 2(λ + 1) < 0⇒ λ∈(−1,∞)              ………. (2)and product of roots =λ2+λ+7>0⇒λ∈R          ……. (3)∴ From (1), (2), (3), we get λ∈[6,∞)(as (1), (2), (3) must be satisfied simultaneously.)Hence, the least value of λ=6.