SOLUTION: Finding all real and imaginary solutions. Problem: w^2 = -225. I only found one solution. Did I do it correctly?

Question 195224: Finding all real and imaginary solutions.
Problem: w^2 = -225. I only found one solution. Did I do it correctly?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

In a word, no. Prove it to yourself. Construct the binomial

where

is the root you calculated. Then square the binomial. If the result is different than

then you can be assured there is another root.

The Fundamental Theorem of Algebra says that a polynomial of degree n has exactly n factors of the form (x - a). Each factor represents a root of the equation. The only way to have a single root for a quadratic is for the polynomial to be a perfect square -- and the only perfect square quadratic polynomials in a single variable are trinomials.

Where you went wrong is that when you took the square root of both sides of your equation, you forgot to consider both the positive and negative roots. Remember that if