Question

Question 4
If $\frac{1}{2}$ is a root of equation $x^2+kx-\frac{5}{4}=0$, then the value of k is
$\left(A\right)2$
$\left(B\right)–2$
$\left(C\right)\frac{1}{4}$
$\left(D\right)\frac{1}{2}$

Answer 1

Given, $\frac{1}{2}$ is a root of the quadratic equation $x^2+kx-\frac{5}{4}=0$
$\Rightarrow {\left(\frac{1}{2}\right)}^2+k\left(\frac{1}{2}\right)-\frac{5}{4}=0$

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