#### Answer

A polynomial equation with real coefficients of degree 3 must have at least on real root.

#### Work Step by Step

According to the Fundamental Theorem of Algebra, a ${{n}^{th}}$ degree polynomial has exactly $n$ roots.
Also, if $f\left( x \right)$ is a polynomial with real coefficients and $x=a+ib$ is a solution of $f\left( x \right)=0$ then $x=a-ib$ is also a solution of $f\left( x \right)=0$.
Thus, a cubic equation can have one real root and two complex roots or it can have three real roots.
Therefore, a cubic equation must have at least one real root.