Question

HELP PLEASE!!!!Which of the following is a polynomial with roots:

Answer 1

Answer:

$P(x) = x^{3} - 2x^{2} -3x + 6$ is the desired polynomial.

Step-by-step explanation:

The roots of the  polynomial is $\sqrt{3}, -\sqrt{3}$  and 2.

Hence, the zeroes of the polynomial with respective roots is:

$(x - \sqrt{3}), (x + \sqrt{3} ) and (x -2)$

Now, if we multiply all the zeroes, we get the desired polynomial.

$P(x) = (x - \sqrt{3})(x + \sqrt{3} )(x -2)$

or, $P(x) = (x^{2} - 3)(x-2) = x^{3} - 2x^{2} -3x + 6$

or, $P(x) = x^{3} - 2x^{2} -3x + 6$

Hence, option D is the correct option.