Question

If alpha is the root of the equation 2x(2x+1)=1, then the other root is?

Answer 1

$2x(2x + 1) = 1 \\ 4 {x}^{2} + 2x - 1 = 0 \\ x = \frac{ - b + - \sqrt{d} }{2a} \\ x = \frac{ - 2 + - \sqrt{4 + 16} }{8} \\ \\ = x = \frac{ - 2 + - \sqrt{20}}{8} \\ = \frac{ - 2 + - 2 \sqrt{5} }{8} \\ \alpha = \frac{ - 1 + \sqrt{5} }{4} \\ \beta = \frac{ - 1 - \sqrt{5} }{4}$