Problem

Complete the sentence below.
If 7+5i is a zero of a polynomial function of degree 5 with real coefficients, then so is

Answer

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Answer

Final Answer: The conjugate of 7+5i, which is 7−5i, is also a zero of the polynomial function of degree 5 with real coefficients.

Steps

Step 1 ：The complex roots of a polynomial with real coefficients always come in conjugate pairs. This is because the coefficients of the polynomial are real numbers, and when you multiply out (a + bi)(a - bi), you get a real number.

Step 2 ：Therefore, if 7+5i is a root of the polynomial, then its conjugate, 7−5i, must also be a root.

Step 3 ：Final Answer: The conjugate of 7+5i, which is 7−5i, is also a zero of the polynomial function of degree 5 with real coefficients.

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