## Precalculus (6th Edition) Blitzer

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 $f\left( x \right)=0$. Hence, we can say that 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.