Question

find the quadratic equation one of whose roots is 2+root 5

Answer 1

$roots \: are \: 2 + \sqrt{5} \\ and \: \\ 2 - \sqrt{5}$

sum of roots

$\alpha + \beta = 4$

product of roots

$\alpha \beta = 4 - 5 = - 1$

quadratic equation is

$x {}^{2} - ( \alpha + \beta )x + \alpha \beta = 0$

$x {}^{2} - 4x - 1 = 0$