The value of discriminant $D$ of the quadratic equation $25x^{2} - 10x + 1 = 0$ is ..... .

Find the discriminant of the following quadratic equation: $9x^{2} - bx + 3 = 0$.

Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $4x^{2} + x - 3 = 0$

Check whether the equation $6x^2 - 7x + 2 = 0$ has real roots, and if it has, find them by the method of completing the squares.

Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $x^{2} + x + \frac{1}{4} = 0$.

Find the nature of the roots of the following quadratic equation. If real roots exist,find them:
$3x^2 - 4\sqrt{3}x + 4 = 0$