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
(A) 2
(B) – 2
(C) 1/4
(D) 1/2

Answer 1

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