The roots of the equation $3 x^{2} - 2 x - 6 = 0$ are

both negative.

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imaginary roots.

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both positive.

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both of opposite signs.

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Solution

The correct option is D both of opposite signs.
The given equation is $3 x^{2} - 2 x - 6 = 0$ .
For a quadratic equation $a x^{2} + b x + c = 0$ , if $a c < 0$ then the roots are of opposite signs.

Here $a c = - 18$
$\Rightarrow - 18 < 0$
$\Rightarrow$ The roots are of opposite signs

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