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)

$16$

We know that, the only even prime is $2$.

$\therefore 2$ is the root of $x^2-\lambda x+12=0$

$\therefore (2{)}^2-\lambda (2)+12=0$

$\Rightarrow \lambda =8$ ... (i)

and $x^2+\lambda x+\mu =0$ has equal roots.

The roots are equal only when discriminant $D=0$ i.e. $b^2-4ac=0$

$\therefore {\lambda }^2-4\mu =0$

or $(8{)}^2-4\mu =0$ ....... [from Eq. (i)]

$\therefore \mu =16$