The quadratic equation whose roots are $\left(2+i\right)$ and $\left(2-i\right)$  is

Sum of the roots  $\alpha +\beta =2+i+2-i$

$\alpha +\beta =4$

Product of the roots $\alpha \beta =\left(2+i\right)\left(2-i\right)$

$\alpha \beta =2^2-i^2$

$\alpha \beta =4+1$

$\alpha \beta =5$

Quadratic equation is $x^2-x\left(\alpha +\beta \right)+\alpha \beta =0$

$x^2-4x+5=0$