Question

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

• A. $2$
• B. $-2$
• C. $\frac{1}{4}$
• D. $\frac{1}{2}$

Answer 1

The correct option is A

$2$

Explanation for the correct option:

Compute the required value.

Since, $\frac{1}{2}$ is a root of the given equation. So, $x=\frac{1}{2}$ satisfy the given equation.

Substitute $x=\frac{1}{2}$ in the given equation and solve for $k$.

$$\begin{gathered} {\left(\frac{1}{2}\right)}^2+k\left(\frac{1}{2}\right)-\frac{5}{4}=0 \\ \Rightarrow \frac{1}{4}+\frac{k}{2}-\frac{5}{4}=0 \\ \Rightarrow \frac{k}{2}=\frac{5}{4}-\frac{1}{4} \\ \Rightarrow \frac{k}{2}=1 \end{gathered}$$

Therefore, the value of $k$ is $2$.

Hence, option $A$ is the correct option.