If $x=2$ is one of the solutions of the quadratic equation $k x^{2}+3 x-4=0,$ then what is the value of $k$?

Verify whether the given value of $x$ is a solution of the quadratic equation or not: $\frac{x+1}{x-1} - \frac{x-1}{x+1} = \frac{5}{6}, x = 5$

Find the roots of the following quadratic equation by using the quadratic formula,if they exist: $x^{2}-5x-1=0$

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 ..... .

The denominator of a non-zero ratio is one less than twice the numerator. If the sum of the ratio and its reciprocal is $2 \frac{4}{15},$ find the ratio.

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