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Question
If `1/2` is a root of the equation `x^2 + kx - 5/4 = 0`, then the value of k is ______.
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Solution
If `1/2` is a root of the equation `x^2 + kx - 5/4 = 0`, then the value of k is 2.
Explanation:
Substitute `x = 1/2` into `x^2 + kx - 5/4 = 0`:
`(1/2)^2 + k(1/2) - 5/4 = 0`
⇒ `1/4 + k/2 - 5/4 = 0`
⇒ `k/2 - 1 = 0`
⇒ `k/2 = 1`
⇒ k = 2
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