given the degree and zeros. Degree: 4, zeros; -5 -2i ; 4 multiplicity 2

Question

 Form a polynomial f(x) with real coefficients having the given degree and zeros.
Degree 4; zeros: negative 5 minus 2 i ; 4 multiplicity 2

Answer 1

Note:  If a + bi is a zero, then a - bi is also a zero

The zeroes are:  -5-2i, -5+2i, 4, 4

 

p(x) = (x + 5 + 2i)(x + 5 - 2i)(x-4)²

 

p(x) = (x² + 10x + 29)(x² - 8x + 16)

 

Just finish multiplying this out to get the final polynomial p(x)