Question

I need help with this question please. Also it’s apart of a homework practice fyi

Answer 1

We are given the following zeros of a polynomial

`0,-3,\sqrt[]{2}`

Let us find the polynomial corresponding to these zeros.

Notice that one of the zeros (√2) is irrational which always comes in conjugate pairs

Let us write these zeros in the factored form

`(x)(x+3)(x+\sqrt[]{2})(x-\sqrt[]{2})`

Now, let us expand and simplify the polynomial

`\begin{gathered} (x)(x+3)(x+\sqrt[]{2})(x-\sqrt[]{2}) \\ (x^2+3x)(x+\sqrt[]{2})(x-\sqrt[]{2}) \\ (x^2+3x)(x^2-\sqrt[]{2}x+\sqrt[]{2}x-\sqrt[]{2}\cdot\sqrt[]{2}) \\ (x^2+3x)(x^2-2) \\ x^4-2x^2+3x^3-6x \\ x^4+3x^3-2x^2-6x \end{gathered}`

Therefore, the correct polynomial is the first option.