The given roots are,
[tex]x=0,\text{ 5, }\sqrt[]{3}[/tex]
To write the polynomial equation:
The polynomial equation can be formed by writing the roots like as follows,
[tex]\begin{gathered} x(x-5)(x-\sqrt[]{3})=(x^2_{}-5x)(x-\sqrt[]{3}) \\ =x^3-5x^2-\sqrt[]{3}x^2+5\sqrt[]{3}x \\ =x^3-(5+\sqrt[]{3})x^2+5\sqrt[]{3}x \end{gathered}[/tex]
Hence, the polynomial equation is,
[tex]x^3-(5+\sqrt[]{3})x^2+5\sqrt[]{3}x[/tex]
