Can-you-factor-x-2-x-1-0-

Question Number 171216 by Bagus1003 last updated on 10/Jun/22

C a n y o u f a c t o r :

x^{2} - x - 1 = 0

Commented by MJS_new last updated on 10/Jun/22

just use the formula

x^{2} + p x + q = 0 \Rightarrow x_{1, 2} = - \frac{p}{2} \pm \sqrt{\frac{p^{2}}{4} - q}

\Rightarrow

x^{2} + p x + q = (x - x_{1}) (x - x_{2})

Answered by aleks041103 last updated on 10/Jun/22

x_{1, 2} = \frac{1 \pm \sqrt{1 + 4}}{2} = \frac{1 + \sqrt{5}}{2}, \frac{1 - \sqrt{5}}{2} = φ, - (φ - 1)

\Rightarrow x^{2} - x - 1 = (x - φ) (x + φ - 1)