Question

If one root of the equation $x^2-\lambda x+12=0$ is even prime while $x^2+\lambda x+\mu =0$ has equal roots, then $\mu$ is equal to

• A. 8
• B. 16
• C. 24
• D. 32

Answer 1

Answer: (B)

We know that, only even prime is $2.$
Then, $(2{)}^2-\lambda (2)+12=0$
$\Rightarrow \lambda =8\dots$...(i)
and $x^2+\lambda x+\mu =0$
has equal roots.
$\therefore {\lambda }^2-4\mu =0$
or$(8{)}^2-4\mu =0$ [from Eq. (i)]
$\therefore \mu =16$