Write a polynomial function having these roots: 1, +/- 2√3, -1, 4

Answer 1

(x-1)(x+1)(x-4)(x+2sqr3)(x-2sqr3)

= (x^2-1)(x-4)(x^2-12)

= (x^3-4x^2-x+4)(x^2-12)

=x^5 -x^4-12x^3+52x^2+12x-48

just take each root, change its sign, then add x to it to get a factor. Then multiply all the factors together.