Question

Form a polynomial f(x) with real coefficients having the given degree and zeros.

Degree 4, zeros 4+4i; -1 multiplicity 2

Enter the polynomial

f(x)=a

Answer 1

If 4+4i is a zero then 4-4i must also be a zero since complex zeros come in conjugate pairs that way and the multiplicity of a zero tells how many times it occurs, so...

f(x) =a ((x - (4+4i)(x - (4 - 4i) (x - (-1))^2 )

Multiply these factors together

 

f(x) = a (x^4 - 6x^3 + 17x^2  + 56x + 32)

Comments

Check the updated answer...