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Q.

The roots of the equation $4 \sqrt{3} x^{2} + 5 x - 2 \sqrt{3} = 0$ are [[1]] and [[2]].

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answer is - 2 3, 3 4.

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Detailed Solution

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The roots of the equation

4 \sqrt{3} x^{2} + 5 x - 2 \sqrt{3} = 0

are

- \frac{2}{\sqrt{3}}

and

\frac{\sqrt{3}}{4}

.
Given quadratic equation is,

4 \sqrt{3} x^{2} + 5 x - 2 \sqrt{3} = 0

.
Then,

4 \sqrt{3} x^{2} + 5 x - 2 \sqrt{3} = 0

⟹ 4 \sqrt{3} x^{2} + 5 x - 2 \sqrt{3} = 0

⟹ 4 \sqrt{3} x^{2} + 8 x - 3 x - 2 \sqrt{3} = 0

⟹ 4 x (\sqrt{3} x + 2) - \sqrt{3} (\sqrt{3} x + 2) = 0

⟹ (\sqrt{3} x + 2) (4 x - \sqrt{3}) = 0

⟹ \sqrt{3} x + 2 = 0 or 4 x - \sqrt{3} = 0

∴ x = - \frac{2}{\sqrt{3}} or x = \frac{\sqrt{3}}{4}

Therefore, the roots of the equation

4 \sqrt{3} x^{2} + 5 x - 2 \sqrt{3} = 0

are

- \frac{2}{\sqrt{3}}

and

\frac{\sqrt{3}}{4}

.

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