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

Answer: (A)

$2$

Substituting $x=\frac{1}{2}$ in given equation, we get

$x^2+kx-\frac{5}{4}=0$

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

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

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

$\therefore k=2$