A polynomial of minimum degree has rational coefficients and has the roots: $x_1=-1-\sqrt5;x_2=1+2i$ so there are $x_3=-1+\sqrt5$ and $x_4=1-2i$. I need to find the polynomial equation.
I tried to use $(x-x_1)(x-x_2)(x-x_3)(x-x_4)$ but the calculations are too "heavy" and too long.There is an easier method to solve this?
Right answer: $x^4-3x^2+18x-20$
Best Answer
$(x+1+\sqrt 5) (x+1+\sqrt 5)=(x+1)^{2}-5$ and $(x-1+2i)(x-1-2i)=(x-1)^{2} +4$. Now multiply $(x+1)^{2}-5$ and $(x-1)^{2} +4$.