Question

identify the simplest polynomial function having integer coefficients with the given zeros. 0, -3, sqrt 2

Answer 1

`x^4+3x^3-2x^2-6x`

Explanation:

0 is a solution of x=0

-3 is a solution of x+3=0

√2 is a solution of x²-2=0

Thus, if these are the factors of the polynomial, then the simplest polynomial function with integer coefficients would be:

`x(x+3)(x^2-2) = (x^2+3x)(x^2-2) = x^4-2x^2+3x^3-6x=x^4+3x^3-2x^2-6x`