Question

Write a polynomial function of least degree with integral coefficients that has the given zeros.​

Answer 1

x^3 -2x^2 -3x+6

Explanation:

We have three roots

Using the root theorem

(x-sqrt(3)) (x- -sqrt(3)) (x-2)

(x-sqrt(3)) (x+sqrt(3)) (x-2)

We know that (x-a) (x+a) = x^2 -a^2

(x^2 -3)(x-2)

FOIL

first x^3

outer -2x^2

inner -3x

last 6

Add these together

x^3 -2x^2 -3x+6