The quadratic equation $2x^{2} - \sqrt{5}x + 1 = 0$ has

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 ..... .

State whether the quadratic equation $3 x^{2}-4 x+1=0$ has two distinct real roots. Justify your answer.

$A$ train,travelling at a uniform speed for $360\, km$,would have taken $48\, min$ less to travel the same distance,if its speed were $5\, km/h$ more. Find the original speed of the train (in $km/h$).

If the following quadratic equation has two equal and real roots,then find the value of $k$: $k x^{2} - 2 \sqrt{5} x + 4 = 0$.

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