Find the nature of roots of the quadratic equation $2 x^{3} - 4 x + 3 = 0$

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Solution

Given equation $2 x^{3} - 4 x + 3 = 0$
Comparing with $a x^{2} + b x + c = 0$
$a = 2, b = - 4$ and $c = 3$
Discriminant $(D) = b^{2} - 4 a c$
$= (- 4)^{2} - 4 \times 2 \times 3$
$= 16 - 24$
$= - 8 < 0$
Thus given equation has no roots.

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