The roots of the equation $2 x^{2} + 4 x + 5$ = 0 are .

real & equal

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real & unequal

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not real

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Solution

The correct option is C not real
The nature of the roots of a quadratic polynomial depends upon its discriminant.
The discriminant of a quadratic equation $a x^{2} + b x + c = 0,$ where $a, b$ and $c$ are constants, is given by $b^{2} - 4 a c .$
$∴$ The discriminant of the equation given is
$D = b^{2} - 4 a c = 4^{2} - 4 (2) (5) = - 24$
Since $D < 0,$ the roots of the equation are not real.

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