If $\ldots \ldots \ldots$ then real roots of a quadratic equation do not exist.

If the discriminant of $x^{2}-10x+(2k-1)=0$ is $40$,then $k=$...............

Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $4x^{2} + 11x + 10 = 0$

If the following quadratic equation has two equal and real roots,then find the value of $k$: $x^{2} - kx + 25 = 0$.

If the following quadratic equation has two equal and real roots,then find the value of $k$: $3x^{2} - 18x + k = 0$.

Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify your answer.