Answer: The answer is (C) Patricia is not correct because both 3 – 4i and -11+√2i must be roots.
Step-by-step explanation: Given that (-11-√2i) , (3 + 4i), and 10 are the roots of the polynomial function f(x) that Patricia is studying.
We know that the complex roots of a polynomial function always occur in pairs. That is, if (a + bi) is a root of a function, then (a – bi) will also be a root (one is the complex conjugate of the other).
The complex conjugate of (3 + 4i) is (3 – 4i) and the complex conjugate of (-11 – √2i) is (11 + √2i).
Therefore, (3 – 4i) and (-11 + √2i) both are the roots of f(x).
Hence, since we have 5 roots, so the degree of the polynomial function f(x) cannot be 4.
Since Patricia concludes that the degree of f(x) is 4, so she is not correct because both (3 – 4i) and (-11+√2i) must be roots.
Thus, option (C) is correct.