Which of the following is a polynomial with roots: - sqrt (3), sqrt (3), and 2?

If a root is n, then the polynomial has the factor (x-n)

So any polynomial with these roots, must have the factors (x+sqrt (3)) (x-sqrt (3)) (x+2)

Since these are cubic polynomials (highest x term is x^3), these are all the factors, so the polynomial is of the form:

k (x+sqrt (3)) (x-sqrt (3)) (x+2)

And since the x^3 term is 1, the constant k must be 1.

So, the polynomial must be the one which is equal to:

(x+sqrt (3)) (x-sqrt (3)) (x+2)

Since the constant term (the last term) is different for each of your 4 options, you just need to evaluate the constant term and see which one matches.

i. e. the answer is whichever polynomial has a constant term equal to

sqrt (3) times (-sqrt (3)) times 2