Question

write the polynomial whose zeroes are
$2 - \sqrt{3 \: } and \: 2 + \sqrt{3}$

Answer 1

$Sum \: of \: zeroes \: (\alpha + \beta )= \: 2 - \sqrt{3} + 2 + \sqrt{3} = 4 \\ Product \: of \: zeroes \: ( \alpha \beta ) = (2 - \sqrt{3} )(2 + \sqrt{3} ) = {2}^{2} - ({ \sqrt{3} })^{2} = 4 - 3 = 1 \\ \\ {x}^{2} - ( \alpha + \beta )x + (\alpha \beta ) \\ {x}^{2} - 4x + 1$