Question

If equation $a{x}^2+bx+c$ = 0 has only imaginary roots and c < 0, then a is ______.

• A. positive
• B. negative
• C. Zero
• D. Can’t say

Answer 1

The correct option is B

negative

If $a{x}^2+bx+c$ = 0 has only imaginary roots,

D <0

$b^2-4ac<0$

$b^2<4ac$

$b^2>0$ and $4ac>b^2\Rightarrow 4ac>0$

$\Rightarrow ac>0$

i.e., 'a' and 'c' has equal signs.

So, as c < 0, a is also less than zero

$\Rightarrow a<0$ (Negative)