enter the poly nomial

Question

Degree 4; zeros: 3 plus 3 i ; 1 multiplicity 2

 

a(x-2i)(x-5)(x+5)(x+5)(x-5)

ax^5-2ax^4-50ax^3+100ax^2+625ax-1250ai

this doesnt feel right, what am i dong wrong

Answer 1

If the coefficients are real, then the complex conjugate of a complex zero must also be a zero.  Then the 4 zeros are:

 

3 + 3i

3 - 3i

1

1

 

The polynomial becomes

 

f(x) = A[x - (3 + 3i)][x - (3 - 3i)](x - 1)²

 

where A is any real number ≠ 0.  You can expand it to standard form if you wish.