Question

If $\frac{1}{2}$ is the 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)

$2$

Given: quadratic equation $x^2+kx-\frac{5}{4}=0$ and $\frac{1}{2}$ is the root of this equation

As $\frac{1}{2}$ is the root of the equation then,

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

i.e., $\frac{1}{4}+\frac{k}{2}-\frac{5}{4}=0$

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

$\Rightarrow 1+2k-5=0$

$\Rightarrow 2k=4$

$\Rightarrow k=2$