Question

f(x) is a polynomial function of degree 4 whose coefficients are real numbers; two of its zeros are -3 and 4 - i. Explain why one of the remaining zeros must be a real number. Write down one of the missing zeros.

Short answer

As the degree of the polynomial is 4 and two of the roots are 3 and 4-i hence by conjugate pairs property one unknown root is 4+i hence we are left with only one unknown root hence that root has to be real root

Step-by-step solution

Given information

We are given a statement, f(x) is a polynomial function of degree 4 whose coefficients are real numbers; two of its zeros are -3 and 4 - i. Explain why one of the remaining zeros must be a real number. Write down one of the missing zeros.

Explain 

As the degree of the polynomial is 4 and two of the roots are 3 and 4-i hence by conjugate pairs property one unknown root is 4+i hence we are left with only one unknown root hence that root has to be real root