Question

If the product of the roots of equation 2$x^2$ + ax + 4 sin a = 0 is 1, then roots will be imaginary if :

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

$\frac{4sina}{2}$ = 1 $\Rightarrow$ sin a = $\frac{1}{2}$

Root are imaginary $\Rightarrow$ $a^2$ - 32 sin a < 0

$\Rightarrow$ $a^2$ < 16

$\Rightarrow$ |a| < 4

$\therefore$ a = $\frac{\pi }{6},\frac{5\pi }{6}.\frac{-7\pi }{6}$