Implicit in SMR 1.2a, is the need to articulate (1) a proof of why the graph of a linear inequality is a half plane and (2) a proof of the fact that the graph of a linear function is a straight line. The latter proof requires the use of basic properties of similar triangles.

The proof of the result that the roots of real polynomials come in complex conjugate pairs (SMR 1.2b) allows one to see how to make use of the Fundamental Theorem of Algebra in a nontrivial way. In the process, one gains a better understanding of both the Fundamental Theorem of Algebra and the Quadratic Formula.

**Please read carefully the following summary description of this topic.** Don't worry if you don't yet understand it completely, or, if you have already studied this material, check your understanding with the practice problems at the end and move on to the next topic.