Answer:
[tex]P(x)=x^{5} +x^{4} -5x^{3} +3x^{2}[/tex]
Step-by-step explanation:
Each root corresponds to a linear factor, so we can write:
[tex]P(x)=x^{2} (x-1)^{2} (x+3)\\=x^{2} (x^{2} -2x+1(x+3)\\\\=x^{5} +x^{4} -5x^{3} +3x^{2}[/tex]
Any polynomial with these zeros and at least these multiplicities will be a multiple (scalar or polynomial) of this [tex]P(x)[/tex]
Footnote
Strictly speaking, a value of [tex]x[/tex] that results in [tex]P(x)=0[/tex] is called a root of
[tex]P(x)=0[/tex] or a zero of [tex]P(x)[/tex] . So the question should really have spoken about the zeros of [tex]P(x)[/tex] or about the roots of [tex]P(x)=0[/tex]
