Question

$if \: 2 + \sqrt{5 \: } and \: 2 - \sqrt{5 \: } are \: the \: zeros \: of \: a \: polynomial \: then \: find \: the \: polynomial$

Answer 1

Solution:-

By Quadratic Formula,

$= {x}^{2} - ( \alpha + \beta )x + \alpha \beta = 0 \\ \\ here \: \: 2 + \sqrt{5} \: \: is \: \: \alpha + \beta \: \: and \: \: \: 2 - \sqrt{5} \: \: \: is \: \alpha \beta \\ \\ = > {x}^{2} - ( 2 + \sqrt{5}) x \: + 2 - \sqrt{5}$