The zeroes of the polynomial is given as,
[tex]0\text{ , 4 and }\sqrt[]{3}[/tex]
The polynomials with the given zeroes is calculated as,
[tex]\begin{gathered} P\mleft(x\mright)=(x-0)(x+4)(x-\sqrt[]{3})(x+\sqrt[]{3}) \\ P(x)=(x^2-3)(x^2\text{ + 4x )} \end{gathered}[/tex]
Thus the required polynomial is,
[tex]P(x)=x^4+4x^3-3x^2-12x^{}[/tex]
