Answer:
[tex]P(x) = x^{3} - 2x^{2} -3x + 6[/tex] is the desired polynomial.
Step-by-step explanation:
The roots of the polynomial is [tex]\sqrt{3}, -\sqrt{3}[/tex] and 2.
Hence, the zeroes of the polynomial with respective roots is:
[tex](x - \sqrt{3}), (x + \sqrt{3} ) and (x -2)[/tex]
Now, if we multiply all the zeroes, we get the desired polynomial.
[tex]P(x) = (x - \sqrt{3})(x + \sqrt{3} )(x -2)[/tex]
or, [tex]P(x) = (x^{2} - 3)(x-2) = x^{3} - 2x^{2} -3x + 6[/tex]
or, [tex]P(x) = x^{3} - 2x^{2} -3x + 6[/tex]
Hence, option D is the correct option.
