Multiple choice

If $\dfrac{1}{2}$ is the root of the equation $x^{2}+kx-\dfrac{5}{4}=0$ then the value of $k$ is :

  1. $2$
  2. $-2$
  3. $\dfrac{1}{4}$
  4. $\dfrac{1}{2}$
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A Correct answer
Explanation

Substitute x = 1/2 into the equation: (1/2)^2 + k(1/2) - 5/4 = 0. 1/4 + k/2 - 5/4 = 0. k/2 - 1 = 0. k/2 = 1, so k = 2.

AI explanation

Because 1/2 is a root of the equation x^2 + kx - 5/4 = 0, substitute x = 1/2 into the equation to get (1/2)^2 + k(1/2) - 5/4 = 0. Simplifying this results in 1/4 + k/2 - 5/4 = 0, which becomes k/2 - 1 = 0. Solving for k yields k = 2.

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