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Q.

Equal root of the equation $2 x^{2} - x + \frac{1}{8} = 0$ is [[1]].

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Detailed Solution

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Equal roots of the equation

2 x^{2} - x + \frac{1}{8} = 0

are

\frac{1}{4}

.
Given quadratic equation is,

2 x^{2} - x + \frac{1}{8} = 0

Then,

2 x^{2} - x + \frac{1}{8} = 0

⟹ 16 x^{2} - 8 x + 1 = 0

⟹ 16 x^{2} - 4 x - 4 x + 1 = 0

⟹ 4 x (4 x - 1) - (4 x - 1) = 0

⟹ (4 x - 1) (4 x - 1) = 0

⟹ 4 x - 1 = 0 or 4 x - 1 = 0

⟹ x = \frac{1}{4} or ⟹ x = \frac{1}{4}

Therefore, equal roots of the equation

2 x^{2} - x + \frac{1}{8} = 0

is

\frac{1}{4}

.

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