The roots of the quadratic equation $\displaystyle 2x^2 - x + \frac{1}{8} = 0$ are
- The roots are $\displaystyle \frac{2}{3}, \frac{3}{4}$.
- The roots are $\displaystyle \frac{1}{4}, \frac{1}{4}$.
- The roots are $\displaystyle \frac{1}{2}, \frac{3}{2}$.
- The roots are $\displaystyle \frac{5}{2}, \frac{2}{7}$.
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B
Correct answer
Explanation
The equation 2x^2 - x + 1/8 = 0 can be multiplied by 8 to get 16x^2 - 8x + 1 = 0. This factors as (4x - 1)^2 = 0, which gives x = 1/4 as a repeated root.
AI explanation
Multiply the entire equation 2x squared minus x plus 1 divided by 8 equals 0 by 8 to clear the fraction, resulting in 16x squared minus 8x plus 1 equals 0. Using the factorisation method, we split the middle term into negative 4x minus 4x because their product is 16 times 1. The equation becomes (4x minus 1)(4x minus 1) equals 0, which means 4x minus 1 equals 0. Solving for x gives x equals 1 divided by 4. The roots are 1 divided by 4 and 1 divided by 4.