Determine the nature of roots of the equation $x^{2} + 2 x \sqrt{3} + 3 = 0$ .

Real and distinct

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Non-real and distinct

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Real and equal

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Non-real and equal

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Solution

The correct option is B Real and equal
The nature of the roots can be determined from the discriminant $b^{2} - 4 a c$
$∴ b^{2} - 4 a c = (2 \sqrt{3})^{2} - (4 \times 1 \times 3)$
$\Rightarrow b^{2} - 4 a c = 12 - 12$
$\Rightarrow b^{2} - 4 a c = 0$
$∵ b^{2} - 4 a c = 0$
There are two real and equal roots.

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