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

-2,5,3+√6

Answer 1

x=3+sqr6

x-3=sqr6

x^2-6x +9= 6

x^2-6x +3= 0

(f(x) = (x+2)(x-5)(x^2 -6x+3)

= (x^2 -3x -10)(x^2-6x+3)

= x^4 -9x^3 +11x -30