Question

How do you find a polynomial function that has zeros `x=0, sqrt3, -sqrt3` and degree n=3?

Answer 1

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

Explanation:

`"since the zeros are "x=0,x=sqrt3,x=-sqrt3" then"`

`"the factors are "x,(x-sqrt3),(x+sqrt3)`

`"the polynomial is then the product of the factors"`

`rArrp(x)=x(x-sqrt3)(x+sqrt3)`

`color(white)(rArrp(x))=x(x^2-3)`

`color(white)(rArrp(x))=x^3-3xlarr" is a possible polynomial"`