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

We have,x2+2(λ+1)x+λ2+λ+7=0Both roots are negative, thenD≥0∴4(λ+1)2−4(λ2+λ+7)≥0⇒λ−6≥0⇒λ∈[6,∞)………………..(i)Sum of roots s=−2(λ+1)<0⇒ λ∈(−1,∞)……………………………..(ii)and product of roots =λ2+λ+7>0⇒ λ∈R………………………………………(iii)∴From (il, (ir) and (iir), we getλ∈[6,∞)The least value of λ=6