Which of the following is true for the coefficients and constant term of a quadratic equation $ax^2 + bx + c = 0$?

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

If $3$ is a root of the quadratic equation $x^{2}-kx+6=0$,then $k = \ldots$

Solve the following equation using the method of 'completing the square': $x^{2}+3x-5=0$.

$A$ rectangular park is to be designed whose breadth is $3\, m$ less than its length. Its area is to be $4\, m^2$ more than the area of a park that has already been made in the shape of an isosceles triangle with its base as the breadth of the rectangular park and of altitude $12\, m$ (see Figure). Find its length and breadth.

Obtain the roots of the following equation using the method of 'completing the square': $16x^{2} - 24x - 1 = 0$.