Question

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.

5, -3, and -1 + 2i

Answer 1

zeros are 5,-3,-1+2 i,-1-2 i (because imaginary roots always occur in pairs)
required polynomial =(x-5)(x+3)(x+1-2i)(x+1+2i)=?
[{x+1-2i}{x+1+2i}={(x+1)-2i}{(x+1)+2i}=(x+1)^2-(2i)^2=x^2+2x+1-4i^2
=x^2+2x+1+4=x^2+2x+5}
required polynomial=(x-5)(x+3)(x^2+2x+5)
simplify .