Choose the correct answer from the given four options in the following questions:
If $ \frac{1}{2} $ is a root of the equation $ x^{2}+k x-\frac{5}{4}=0 $, then the value of $ k $ is

(A) 2
(B) $ -2 $
(C) $ \frac{1}{4} $
(D) $ \frac{1}{2} $

Given:

\( \frac{1}{2} \) is a root of the equation \( x^{2}+k x-\frac{5}{4}=0 \).

To do:

We have to find the value of $k$.

Solution:

$\frac{1}{2}$ is a root of the quadratic equation $x^{2}+k x-\frac{5}{4}=0$

This implies,

$(\frac{1}{2})^{2}+k(\frac{1}{2})-\frac{5}{4}=0$

$\frac{1}{4}+\frac{k}{2}-\frac{5}{4}=0$

$\frac{1+2 k-5}{4}=0$

$2 k-4=0$

$2 k=4 $

$k=2$

The value of $k$ is 2.

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Updated on: 10-Oct-2022

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