Write a polynomial function of least degree

Question

integral coefficients whose zeros include: -6, 0, 0.5, 3, -5i, 2+2i

Answer 1

Imaginary (-5i) and complex (2+2i) roots always come in conjugate pairs, so 5i and 2-2i are also roots.  In factored form, the simplest polynomial of least degree would be:

 

p(x) = (x+6)*x*(x-0.5)*(x-3)*(x+5i)*(x-5i)*(x-(2+2i))*(x-(2-2i))

 

This is an 8th degree polynomial.  Multiply it out to put it into standard form.  Hint:

• (x+5i)(x-5i) = x²+25
• (x-(2+2i)(x-(2-2i) = (x²+8)