Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. Write the function in standard form

Question

1,2-√3

Answer 1

x = 2-sqr3

x-2 = -sqr3

x^2 -4x + 4 = 3

x^2-4x +1 = 0

f(x) = (x-1)(x^2 -4x+1)

= x^3 -5x^2+5x -1

Answer 2

P(x) = (x - 1)(x - (2 - √3))(x - (2 + √3))