If one of the roots of $2x^{2}-5x+k=0$ is $\frac{7}{2}$,then $k=$ .............

Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $x^{2} = 9$.

If one of the roots of the equation $kx^{2} + 2x - 3 = 0$ is $2$,then find $k$.

If one of the roots of $x^{2}-2x-c=0$ is $5$,the other root is ...........

Solve the following equation using the quadratic formula,if the equation has a solution in $R$: $\frac{1}{x+1} + \frac{2}{x+2} = \frac{4}{x+4}; \, x \neq -1, -2, -4$.

Examine whether the following equation is quadratic or not: $\sqrt{2} x^{2}-5 \sqrt{3} x+6=0$