Question

If the equation \( x^2 + λx + μ = 0 \) has equal roots and one root of the equation \( x^2 + λx -12 = 0 \) is 2, then (λ, μ) =

Answer 1

we have equal roots, therefore \( λ^2 = 4μ \).

Now second equation \( x^2 + λx - 12 = 0 \) has a root 2, so put

x = 2 ⇒ 4 + 2λ - 12 = 0 ⇒ λ = 4

Hence from \( λ^2 = 4μ \), we have μ = \(\frac{16}{4}\) = 4

⇒ (λ, μ) = (4, 4)