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

positive

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negative

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Zero

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Can’t say

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Solution

The correct option is B
negative

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

D <0

$b^{2} - 4 a c < 0$

$b^{2} < 4 a c$

$b^{2} > 0$ and $4 a c > b^{2} \Rightarrow 4 a c > 0$

$\Rightarrow a c > 0$

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

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

$\Rightarrow a < 0$ (Negative)

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