Question

Form the equation whose roots are $\pm 4\sqrt{3},5\pm 2\sqrt{-1}$.

Answer 1

$\pm 4\sqrt{3},5\pm 2\sqrt{-1}=5\pm 2i$

The equation with given roots is

$(x+4\sqrt{3})(x-4\sqrt{3})\{x-(5+2i\left)\right\}\{x-(5-2i\left)\right\}=0(x^2-48)\left\{\right(x-5)-2i)\left\}\right\{(x-5)+2i\left)\right\}=0(x^2-48)\{{(x-5)}^2-4i^2\}=0(x^2-48)(x^2+25-10x+4)=0(x^2-48)(x^2+29-10x)=0x^4+29x^2-10x^3-48x^2+480x-1392=0$