Multiple choice

If one root of the quadratic equation $3y^{2}\,-\,ky\,+\,8\,=\,0$ is $\displaystyle\,\frac{2}{3}$, then find the value of $k$.

  1. 14

  2. 13

  3. 12

  4. 11
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A Correct answer
Explanation

Substitute y = 2/3 into the equation: 3(2/3)^2 - k(2/3) + 8 = 0. 3(4/9) - 2k/3 + 8 = 0. 4/3 - 2k/3 + 8 = 0. Multiply by 3: 4 - 2k + 24 = 0. 28 = 2k, so k = 14.

AI explanation

Substitute the given root y equals two thirds directly into the equation 3y squared minus ky plus 8 equals 0. This gives 3 times two thirds squared minus k times two thirds plus 8 equals 0. Calculating the terms results in four thirds minus two thirds k plus 8 equals 0. Multiplying the entire equation by 3 gives 4 minus 2k plus 24 equals 0, which simplifies to 2k equals 28, so k equals 14.

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