Chapter 8.6, Problem 8OE

To determine

To explain: That the statement is true.

Answer to Problem 8OE

The statement is trueapolynomial with any complex roots must have a number of complex roots which is a multiple of 2 as any equation with $x+iy$ as a root must $x-iy$ as a root (its complex conjugate).

Explanation of Solution

Given information:

Every third-degree polynomial equation with real coefficient has at least one real root.

A polynomial with any complex roots must have a number of complex roots which is a multiple of 2 as any equation with $x+iy$ as a root must $x-iy$ as a root (its complex conjugate).

Therefore, a polynomial of highest degree 5 must have at least 1 real root

Hence,

The statement is true.