Question

Write the polynomial function of minimum degree in standard form with real coefficients whose zeros include 1,1-i ,1=i ?

Answer 1

$$P(x)=a(x-x_1)(x-x_2)(x-x_3)$$

Let $a=1.$ Then

$$P(x)=(x-1)(x-(1-i))(x-(1+i))$$

$$P(x)=(x-1)(x^2-2x+2)$$

$$P(x)=x^3-2x^2+2x-x^2+2x-2$$

$$P(x)=x^3-3x^2+4x-2$$