Question

高次多项函数write the equation of lowest degree with real coeffici

Answer 1

因为为这个方称的根1+i为根,因为conjugate原理,1-i也为这个方程的根

(x+1)(x-1-i)(x-1+i)=0

(x+1)(x^2-x+ix-x+1-i-ix+i+1)=0

(x+1)(x^2-2x+2)=0

(x^3-2x^2+2x+x^2-2x+2)=0

x^3-x^2+2=0