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

The value of the discriminant of a quadratic equation $kx^{2} - 4x - 4 = 0$ is $64$,then $k = \dots$

The discriminant of the equation $3x^2 - 6x + 4 = 0$ is .............

If the roots of the quadratic equation $x^{2}+8x+3=0$ exist,find them using the method of completing the square.

Verify whether the given value of $x$ is a solution of the quadratic equation or not: $x + \frac{1}{x} = 3 \frac{1}{3}$; $x = \frac{1}{3}$.

The name of the Indian mathematician who gave the formula for finding the roots of the quadratic equation $ax^2 + bx + c = 0$ by the method of completing the square is ..... .