Question

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

Answer 1

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

Explanation:

The roots of the polynomial is
`√(3), -√(3)` and 2.

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

`(x - √(3)), (x + √(3) ) and (x -2)`

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

`P(x) = (x - √(3))(x + √(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.