Question

EXTRA POINTS

Write a polynomial function of least degree using the given zeros.

-2, multiplicity of 2, -1+√5.

I am able to get to (x + 2)(x + 2) -> x^2+4x+4

What do I do with the last zero?

What I'm thinking is x = -2+√7 ->

x = -4 + 7 ->

x = 3

Is x = 3 the last zero?

Answer 1

if the problem want rational coefficient, then u need additional zero -1-√5 so you will expand a polynomial
(x+2)(x-2)²(x-1-√5)(x-1+√5). otherwise not necessary ie
(x+2)(x-2)²(x-1-√5).