Question

red mark question
answer fastly dude ​

Answer 1

Answer:

given,

$\alpha = 2 + \sqrt{5} \\ and \: \alpha + \beta = 4 ............i\\ = > \beta = 2 - \sqrt{5} \\ now. \\ \\ \alpha \beta = (2 + \sqrt{5} )(2 - \sqrt{5} ) \\ = 2 ^{2} - 5 = 4 - 5 = 1 \\ \\ now. \\ required \: quadratic \: polynomial \\ = {x}^{2} - ( \alpha \times \beta )x \: + \alpha \beta \\ = {x}^{2} - 4x \: + ( - 1) \\ = {x}^{2} - 4x - 1$