The polynomial with 6 roots is the one of degree 6, so the correct option is:
[tex]f(x) = 7x^6 + 3x^2 + 12[/tex]
You need to remember that if p(x) is a polynomial of degree N, then it has N roots (such that some of these N roots may be equal or not).
Then we just need to find the polynomial of degree 6. (Remember that the degree represents the maximum exponent of the polynomial).
In this case, the only one of degree 6 is:
[tex]f(x) = 7x^6 + 3x^2 + 12[/tex]
Which is the last option.
If you want to learn more about polynomials, you can read:
https://brainly.com/question/4142886
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