A polynomial function f(x) degree 4 with real coefficients has zeros of 3 and 5-i. Explain why one of the remaining zeros must be a real number.

PLEASEEE HEELP!

Question

A polynomial function f(x) degree 4 with real coefficients has zeros of 3 and 5-i. Explain why one of the remaining zeros must be a real number.

PLEASEEE HEELP!

noelgreco · Answer

Each imaginary solution has to come with its complex conjugate, in this case, (5+i).

Since complex solutions come in pairs, and the other solution is real, the fourth solution must be real.  (If it were complex, it would require its complex conjugate.)