Question:
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) $\frac{1}{2}$
Solution:
(a) Since, $\frac{1}{2}$ is a root of the quadratic equation $x^{2}+k x-\frac{5}{4}=0$
Then, $\quad\left(\frac{1}{2}\right)^{2}+k\left(\frac{1}{2}\right)-\frac{5}{4}=0$
$\Rightarrow \quad \frac{1}{4}+\frac{k}{2}-\frac{5}{4}=0 \Rightarrow \frac{1+2 k-5}{4}=0$
$\Rightarrow \quad 2 k-4=0$
$\Rightarrow \quad 2 k=4 \Rightarrow k=2$
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