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Q.

Roots of the equation $3 \sqrt{7} x^{2} + 4 x - \sqrt{7} = 0$ are [[1]] and [[2]].

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answer is - 7 3, 1 7.

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Detailed Solution

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Roots of the equation

3 \sqrt{7} x^{2} + 4 x - \sqrt{7} = 0

are

- \frac{\sqrt{7}}{3}

and

\frac{1}{\sqrt{7}}

.
Given quadratic equation is,

3 \sqrt{7} x^{2} + 4 x - \sqrt{7} = 0

Then,

⟹ 3 \sqrt{7} x^{2} + 4 x - \sqrt{7} = 0

⟹ 3 \sqrt{7} x^{2} - 3 x + 7 x - \sqrt{7} = 0

⟹ 3 x (\sqrt{7} x - 1) + \sqrt{7} (\sqrt{7} x - 1) = 0

⟹ (3 x + \sqrt{7}) - (\sqrt{7} x - 1) = 0

⟹ (3 x + \sqrt{7}) (\sqrt{7} x - 1) = 0

⟹ 3 x + \sqrt{7} = 0 or \sqrt{7} x - 1 = 0

∴ x = - \frac{\sqrt{7}}{3} 0 r x = \frac{1}{\sqrt{7}}

Therefore, roots of the equation

3 \sqrt{7} x^{2} + 4 x - \sqrt{7} = 0

are

- \frac{\sqrt{7}}{3}

and

\frac{1}{\sqrt{7}}

.

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Roots of the equation 37x2+4x-7=0 are [[1]] and [[2]].