Question

Find a third-degree polynomial with real coefficients and the given zeros (i = √-1): -i and -2

Answer 1

x³ +2x² +x +2

1) Since we have -i and -2 we can rewrite them as factors as complex numbers

into a +bi form. So,

Let's pick the conjugate (a -bi) of those numbers and write as factors. We need 3 factors for a 3rd-degree polynomial.

(x+2)(x+i)(x-i) Distribute the factors

(x+2)(x²-i²) Remember and plug i²=-1

(x+2)(x²+1)

x³ +x+2x²+2

x³ +2x² +x +2