2x² + 5 $\sqrt{3}$ x + 16 = 0

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Solution

Given: 2x² + 5 $\sqrt{3}$ x + 16 = 0
To find the nature of the roots, we need to find the discriminant of the given quadratic equation.
We know that the discriminant of a quadratic equation, Δ = b² – 4ac.
On comparing the given equation with ax² + bx + c = 0, we get:
a = 2, b = 5 $\sqrt{3}$ and c = 16
Thus,
Δ = (5 $\sqrt{3}$ )²– 4(2)(16)
$\Rightarrow$ Δ = 75 – 128 = –53
Since Δ < 0, the roots of the given quadratic equation are not real.

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