The golden and silver ratios are the roots of the equation $x^2-x-1=0$: $$\frac{1\pm\sqrt{5}}{2}.$$ They show up in the formula of Fibonacci numbers: $$F_n=\frac{1}{\sqrt{5}}\left(\frac{1+\sqrt{5}}{2}\right)^n+\frac{1}{\sqrt{5}}\left(\frac{1-\sqrt{5}}{2}\right)^n$$
Are the roots of the equation $x^2+x-1=0$ any significant and do they have some special names: $$\frac{-1\pm\sqrt{5}}{2}?$$
EDIT: For $x^2 + x - 1 = 0$, there is nothing really significant or noteworthy about the roots, other than one of them is $-\phi = \dfrac {-1-{\sqrt 5}}{2}$ or $-1.618$, and the other is $\dfrac {1}{\phi} = \dfrac {-1+{\sqrt 5}}{2}$ or $0.618$.