Question

If the roots of the equation ${\lambda }^2+8\lambda +{\mu }^2+6\mu =0$ are real, then $\mu$ lies between

• A. $-2$ and $8$
• B. $-3$ and $6$
• C. $-8$ and $2$
• D. $-6$ and $3$

Answer 1

The correct option is C $-8$ and $2$

For real roots the discriminant must be non-negative,

$D>0$

$8^2-4({\mu }^2+6\mu )>0$

$16-{\mu }^2-6\mu >0$

${\mu }^2+6\mu -16<0$

$(\mu -2)(\mu +8)<0$

$-8\le \mu \le 2$