# 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) $\frac{1}{2}$

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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.

Updated on 10-Oct-2022 13:27:26