The bi-quadratic equation two of whose roots are $1+i,1-\sqrt{2}$  is

Roots $\Rightarrow 1+i,1-i\Rightarrow 1+\sqrt{2},1-\sqrt{2}$

$\alpha +\beta +\gamma +\delta$

$\Rightarrow 1+i+1-i+1-\sqrt{2}+1+\sqrt{2}$

$\Rightarrow 1+1+1+1$

$\Rightarrow 4$

$\alpha \beta \gamma \delta =\left(1^2-i^2\right)\left(1^2-{\left(\sqrt{2}\right)}^2\right)$

$=\left(1+1\right)\left(-1\right)$

$=-2$

$f\left(x\right)=x^4-4x^3+5x^2-2x-2=0$