• # question_answer 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 $(\lambda ,\mu )$= A) (4, 4) B) (-4,4) C) $(4,-4)$ 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 $x=2$Þ $4+2\lambda -12=0$Þ $\lambda =4$ Hence from${{\lambda }^{2}}=4\mu$, we have $\mu =\frac{16}{4}=4$  Þ $(\lambda ,\mu )=(4,4)$.