Question

Solve for x x^2-(root3+1)x+root 3 =0

Answer 1

${x}^{2} - (\sqrt{3} + 1)x + \sqrt{3} = 0. \\ {x}^{2} - \sqrt{3}x - x + \sqrt{3} = 0 \\ x(x - \sqrt{3} ) - 1(x - \sqrt{3}) = 0 \\( x - 1) (x - \sqrt{3} ) = 0 \\ implies \: \: (x - 1) = 0 \: or \: x - \sqrt{3} = 0 \\ \: \: \: \: \: \: \: \: x = 1 \: or \: x = \sqrt{3} .$

Use factorization method to find roots