Find a polynomial of degree n that has only the given zeros

Find a polynomial of degree n that has only the given zero(s). (There are many correct answers.)

x = 0, sqrt(3) , -sqrt(3) ; n = 3

given zeros are

a = 0

b = sqrt 3

c = - sqrt 3

polynomial would be

p(x) = (x-a) (x-b)(x-c)

plugging the values of a,b,c

p(x) = (x-0) (x-sqrt 3) (x-(-sqrt3 ))

p(x) = (x) (x- sqrt 3 ) (x+ sqrt 3)

p(x) = x (x^2 - 3) = x^3 - 3x

hence , polynomial is p(x) = x^3 - 3x