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

Question

x=0,-√5,√5; n=5

Answer 1

zeros 0, sqr5, -sqr5

n=5, degree 5

x=0, x=sqr5, x=-sqr5

x-sqr5= 0, x+sqr5=0, x-0=0

(x-0)(x-sqr5)(x+sqr5) = 0

x(x^2-5) = 0

x^3 -5x = 0

x^3-5x is a polynomial degree 3 with zeros 0, +/-sqr5

also polynomials with a coefficient a, where a is a nonzero integer,

and multiply by x^2 to get degree 5

ax^3(x^2-5)

= ax^5 -5ax^3

specific examples:

x^5 -5x^3

or

2x^5 - 10x^3