If $\frac{1}{2}$ is a root of the equation $x^{2}+kx-\frac{5}{4}=0$,then the value of $k$ is

In a right triangle,the length of the hypotenuse is $2\,cm$ more than the length of the base and $1\,cm$ more than twice the length of the altitude. Find the length of the hypotenuse. (in $,cm$)

Two water taps together can fill a tank in $9 \frac{3}{8}$ hours. The tap of larger diameter takes $10 \text{ hours}$ less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

Find the roots of the following quadratic equation using the quadratic formula,if they exist: $\frac{1}{x+1} + \frac{2}{x+2} = \frac{4}{x+4}$; $(x \neq -1, -2, -4)$

Comparing the quadratic equation $5x^{2}-4x-1=0$ with the standard form $ax^{2}+bx+c=0$,we get $b=\ldots$

Find the roots of the following quadratic equation by the method of completing the square: $x^{2}-(\sqrt{3}+1) x+\sqrt{3}=0$