By Tricia Lobo | Updated August 30, 2022
When exploring algebra and advanced mathematics, you may encounter equations whose solutions involve imaginary numbers, such as i = √-1. In such cases, if the problem specifically requests solutions within the real number system, the imaginary (non‑real) roots must be excluded, leaving only the real ones. After grasping the fundamental method, filtering out non‑real solutions becomes straightforward.
Factor the equation. For example, the cubic 2x³+3x²+2x+3=0 can be rewritten as x²(2x+3)+1(2x+3)=0, and then factored further to (x²+1)(2x+3)=0.
Determine the roots of each factor. Setting x²+1=0 yields x=±√-1 (i.e., x=±i). Setting 2x+3=0 gives the real root x=−3/2.
Discard the non‑real roots. The only acceptable solution in the real number system is x=−3/2.
Thus, by factoring, solving, and discarding the imaginary roots, you can confidently provide the real solutions.
