If a polynomial function, f of x , with rational coefficients has roots 0 , 4 , and 3 plus square root of 11 , what must also be a root of f of x ?

For a polynomial with rational coefficients, any irrational root involving a square root must be accompanied by its conjugate. Since 3 + √11 is a root, 3 − √11 must also be a root. Therefore, the correct choice is B, 3 minus square root of 11.

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