Given is a zero of the polynomial function , find the remaining zeros of the polynomial.
E)5 i, -5, 4 + i , 4 - i

Question

Given  is a zero of the polynomial function  , find the remaining zeros of the polynomial.
E)5 i, -5, 4 + i , 4 - i

Quizplus · Accepted Answer

We know that a polynomial of degree n has n complex zeros (including repeated ones). Since one zero is given, there are 10 remaining zeros. The given zero is a complex number with a real part of 11ebfdc1_ec29_3117_abe3_039ecf21d969 and an imaginary part of TBX8727_11. It's important to note that the other zeros have to be complex conjugates in order for the polynomial to have real coefficients (since complex roots come in conjugate pairs). Therefore, the remaining zeros are 11ebfdc1_ec29_3119_abe3_b12580358a95_TBX8727_11 (the conjugate of the given zero), and the conjugates of the other two roots in choice E. However, since these conjugates are not listed among the answer choices, the only option is to choose the next closest answer choice which has a complex conjugate as a root, which is C.

Given Is a Zero of the Polynomial Function