The equation $9x^2 + 30x + 25 = 0$ has .............. in $R$.

Solve the following equation using the method of factorization and write its solution set: $\frac{x}{x+1} + \frac{x+1}{x} = \frac{41}{20}$

Find the roots of the following quadratic equation by using the quadratic formula,if they exist: $(x+4)(x+5)=3(x+1)(x+2)+2x$

$120$ kites were divided equally among a certain number of children in a school. If there were $4$ children fewer,each child would have received $1$ kite more. Find the number of children.

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

The value of the discriminant of the quadratic equation $5x^{2} + x + 2 = 0$ is ..... .