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Q.

Find the roots of the equation $x^{2} - 3 \sqrt{3} x - 30 = 0$ .

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a

\sqrt{3}

and

- 5 \sqrt{3}

b

2 \sqrt{3}

and

- 5 \sqrt{3}

c

3 \sqrt{3}

and

- 2 \sqrt{3}

d

4 \sqrt{3}

and

- 3 \sqrt{3}

answer is B.

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Detailed Solution

detailed_solution_thumbnail

Given quadratic equation is,

x^{2} - 3 \sqrt{3} x - 30 = 0

.
Then,

⟹ x^{2} + 3 \sqrt{3} x - 30 = 0

⟹ x^{2} + 5 \sqrt{3} x - 2 \sqrt{3} x - 30 = 0

⟹ x (x + 5 \sqrt{3} x) - 2 \sqrt{3} (x + 5 \sqrt{3}) = 0

⟹ (x - 2 \sqrt{3}) (x + 5 \sqrt{3}) = 0

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

∴ x = 2 \sqrt{3} or x = - 5 \sqrt{3}

∴ The roots of the equation are

2 \sqrt{3}

and

- 5 \sqrt{3}

.
Hence, option (2) is correct.

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