Question

If 1 / 2 is a root of the equation x^2 + kx - 5 / 4 = 0 then find the value of k.

Answer 1

x² + kx - 5/4 = 0

Given that 1/2 is a root

⇒ When x = 1/2, the equation returns 0

Solve for k:

(1/2) ² + k(1/2) - 5/4 = 0

1/4 + 1/2 k - 5/4 = 0

1/2 k - 1 = 0

1/2 k = 1

k = 2

Answer: k = 2

Answer 2

Given Equation : x² - Kx - $\dfrac{5}{4}=0$

In the question, given that $\dfrac{1}{2}$ is a root of the question. It means that one value of x is $\dfrac{1}{2}$


$\therefore \: x = \dfrac{1}{2}$



Now, substituting the value of x in the given equation.


$\Rightarrow { \bigg( \dfrac{1}{2} \bigg) }^{2} - k \bigg( \dfrac{1}{2} \bigg) - \dfrac{5}{4} = 0 \\ \\ \\ \Rightarrow \dfrac{1}{4} - \dfrac{k}{2} - \frac{5}{4} = 0 \\ \\ \\ \Rightarrow \dfrac{1 - 2k - 5}{4} = 0 \\ \\ \\ \Rightarrow \: 2k - 4= 0 \\ \\ \Rightarrow 2k = 4 \\ \\ \Rightarrow k = \dfrac{4}{2} \\ \\ \Rightarrow k = 2$



Therefore the value of k satisfying the equation ( when one root is 1 / 2 ) is 2.


Value of k : 2