Question

tell the correct option with solution​

Answer 1

Answer:

Step-by-step explanation:

Given :-

1/2 is the given root of the equation.

To Find :-

Value of k.

Solution :-

This is satisfying the Quadratic Equation,

On Solving the equation, we get

$\bf\implies x^{2}+kx-\dfrac{5}{4}=0$

$\sf\implies (\dfrac{1}{2})^{2}+k(\dfrac{1}{2})-\dfrac{5}{4}=0$

$\sf\implies \dfrac{1}{4}+\dfrac{k}{2}-\dfrac{5}{4}=0$

$\sf\implies \dfrac{1+2k-5}{4}=0$

$\sf\implies 2k-4=0$

$\sf\implies k=\dfrac{4}{2}$

$\bf\implies k=2$

Hence, the value of k is 2.

Answer 2

Answer:

k = 2

Step-by-step explanation:

$\text{Given quadratic equation: } x^2 + kx - \dfrac{5}{4} = 0\\ \\\\\text{It is also given that \dfrac{1}{2} is a root of the given quadratic equation.}\\\\\\\text{So, on replacing the value of x by \dfrac{1}{2} in the above quadratic equation,}\\\\\\\text{we get}\\\\\\\left( \dfrac{1}{2} \right)^2 + k \left( \dfrac{1}{2} \right) - \dfrac{5}{4} = 0\\\\\\\implies \dfrac{1}{4} + \dfrac{1}{2}k - \dfrac{5}{4} = 0\\\\\\\implies \dfrac{1 + 2k - 5}{4} = 0$

$\implies 2k - 4 = 0 \times 4\\\\\implies 2k - 4 = 0\\\\\implies 2k = 0 + 4\\\\\implies 2k = 4\\\\\implies k = \dfrac{4}{2}\\\\\\\implies \boxed{\underline{\boxed{\bold{k = 2}}}}$