Questions: Information is given about a polynomial (f(x)) whose coefficients are real numbers. Find the remaining zeros off. Degree 4; zeros: (i,-7+i) The remaining zero(s) of f is(are) (square) . (Use a comma to separate answers as needed.)

Information is given about a polynomial (f(x)) whose coefficients are real numbers. Find the remaining zeros off. Degree 4; zeros: (i,-7+i) The remaining zero(s) of f is(are) (square) . (Use a comma to separate answers as needed.)
Transcript text: Information is given about a polynomial $f(x)$ whose coefficients are real numbers. Find the remaining zeros off. Degree 4; zeros: $i,-7+i$ The remaining zero(s) of f is(are) $\square$ . (Use a comma to separate answers as needed.) Clear all Check answer
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Solution

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Solution Steps

Step 1: Identify the Complex Zeros

Given zeros are: ['0+1.0i', '-7+1.0i']. After ensuring conjugate pairs, zeros are: ['0+1.0i', '-7+1.0i', '0-1.0i', '-7-1.0i'].

Step 2: Count the Given Zeros

The total count of given zeros, including conjugates, is: 4.

Step 3: Determine the Missing Zeros

The polynomial degree is 4. Given zeros count is 4. Hence, missing zeros count is: 0.

Step 4: Use the Conjugate Zeros Rule

After applying the conjugate zeros rule, the zeros are: ['0+1.0i', '-7+1.0i', '0-1.0i', '-7-1.0i'].

Step 5: Identify Real Zeros if Possible

No missing zeros. All zeros have been identified.

Final Answer:

All zeros of the polynomial have been identified: ['0+1.00i', '-7+1.00i', '0-1.00i', '-7-1.00i'].

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