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 $(\lambda ,\mu )=$

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

Answer 1

The correct option is A

(4,4)

Given: $x^2+\lambda x+\mu =0$ have equal roots, therefore its discriminant should be zero.
$\Rightarrow {\lambda }^2=4\mu$

Now second equation $x^2+\lambda x-12=0$ has a root $x=2$.
put $x=2$ in the equation, we get
$\Rightarrow 4+2\lambda -12=0\Rightarrow \lambda =4$

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