Question

A polynomial of degree at least 3 where all the zeros are positive whole numbers

Answer 1

Answer:

This is one of many possible answers.

(x -1)(x-2)(x-3)

Explanation:

The zeros are x = 1, x = 2, x = 3. This polynomial has a degree of 3.

Answer 2

We can build a polynomial given it's degree and zeros. Below I am going to show how we do that, and then I will solve the question, finding that one example of a desired polynomial is:

$f(x) = x^3 - 15x^2 + 54x - 40$

Zeros of a function:

Given a polynomial f(x), this polynomial has roots $x_{1}, x_{2}, x_{n}$ such that it can be written as: $a(x - x_{1})*(x - x_{2})*...*(x-x_n)$, in which a is the leading coefficient.

In this question:

Polynomial of degree 3, so 3 roots.

All positive, I will choose:

$x_1 = 1, x_2 = 4, x_3 = 10$

I will choose the leading coefficient as a = 1.

Thus

$f(x) = a(x - x_1)(x - x_2)(x - x_3)$

$f(x) = (x-1)(x-4)(x-10)$

$f(x) = (x^2-5x+4)(x-10)$

$f(x) = x^3 - 15x^2 + 54x - 40$

The image shown in the end of this question shows that this polynomial has three positive roots, also all whole numbers.

Another similar example is given at https://brainly.com/question/21328461