Prove the following


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) $\frac{1}{2}$


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

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

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

$\Rightarrow \quad 2 k-4=0$

$\Rightarrow \quad 2 k=4 \Rightarrow k=2$

Leave a comment


Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now