Degree​ 4; ​ zeros: negative 3 minus 3 i ; minus 1 multiplicity 2

Question

Degree​ 4; ​ zeros:

negative 3 minus 3 i ; minus 1−3−3i; −1

multiplicity 2

Answer 1

A polynomial with degree 4 will have 4 roots, including complex roots and double roots

(-3 - 3i) is root means is complex conjugate (-3 + 3i) is also a root

above means (x -(-3 -3i)) and (x - (-3 + 3i)) are factors of the polynomial

-1 is a root of multiplicity of 2 means (x + 1)^2 is a factor

so polynomial p(x)=A(x-(-3-3i))(x-(-3+3i))(x+1)^2 where A is a constant which can be found if we know a point on the graph of the polynomial

simpilying the above will give the following,

p(x)=A(x^2 + 6x + 18)(x + 1)^2