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Q.

The roots of the equation $x^{2} - 3 \sqrt{5} x + 10 = 0$ are [[1]] and [[2]].

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answer is 5, 2 5.

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Detailed Solution

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The roots of the equation

x^{2} - 3 \sqrt{5} x + 10 = 0

are

\sqrt{5}

and

2 \sqrt{5}

.
Given quadratic equation is,

x^{2} - 3 \sqrt{5} x + 10 = 0

Then,

x^{2} - 3 \sqrt{5} x + 10 = 0

⟹ x^{2} - 2 \sqrt{5} x - \sqrt{5} x + 10 = 0

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

⟹ (x - \sqrt{5}) (x - 2 \sqrt{5}) = 0

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

∴ x = \sqrt{5} or x = 2 \sqrt{5}

Therefore, the roots of the equation

x^{2} - 3 \sqrt{5} x + 10 = 0

are

\sqrt{5}

and

2 \sqrt{5}

.

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