Question

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

• A. (-4,4)
• B. (-4, -4)
• C. (4, -4)
• D. (4, 4)

Answer 1

The correct option is D

(4, 4)

we have equal roots, therefore ${\lambda }^2=4\mu$.

Now second equation $x^2+\lambda x-12=0$ has a root 2, so put

x = 2 ⇒ 4 + 2λ - 12 = 0 ⇒ λ = 4

Hence from ${\lambda }^2=4\mu$, we have μ = $\frac{16}{4}$ = 4

⇒ (λ, μ) = (4, 4)