The golden number $\frac{1+\sqrt{5}}{2}$ is one of the solutions of ...... .

Solve the following quadratic equation using the quadratic formula,if the equation has a solution in $R$: $x^{2}+5x+3=0$.

Examine whether the following equation is quadratic or not: $x - \frac{1}{x} = 5$

Find the roots of the following quadratic equation using the quadratic formula,if they exist: $\frac{1}{x+1} + \frac{2}{x+2} = \frac{4}{x+4}$; $(x \neq -1, -2, -4)$

In a right triangle,the length of the hypotenuse is $2\,cm$ more than the length of the base and $1\,cm$ more than twice the length of the altitude. Find the length of the hypotenuse. (in $,cm$)

The standard form of a quadratic equation in one variable is $\ldots \ldots \ldots \ldots . .$