Multiple choice

If 1 2 is a root of the equation x2 + kx - 5 4 = 0, then the value of k is

  1. 2
    • 2

  3. 1 4

  4. 1 2
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A Correct answer
Explanation

Interpreting the garbled root as 1/2 and the constant term as -5/4, substitute x = 1/2 into the equation. This gives 1/4 + k/2 - 5/4 = 0, so k = 2.

AI explanation

Substitute the given root one-half into the equation x2 + kx - five-fourths = 0, resulting in the equation one-fourth plus k divided by 2 minus five-fourths equals 0. Simplifying this gives k divided by 2 minus 1 equals 0. Solving for k shows that k divided by 2 equals 1, so k equals 2.

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