State the nature of the given quadratic equation $2 x^{2} + 6 x + \frac{9}{2} = 0$

Real and Distinct roots

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Real and equal roots

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Imaginary roots

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None of the above

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Solution

The correct option is B Real and equal roots
$D = b^{2} - 4 a c$
$D = 36 - (4) (2) (\frac{9}{2})$
$D = 0$
Therefore, the quadratic equations has equal roots.

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