In school we're learning to use the quadratic formula. I understand how to use it and what its applications are, but I don't understand why sometime it's okay to simplify and sometimes it's not. For example, I got the result (-2 ± 2 square root of 6)/2. According to the back of my book, this is the correct answer. I would normally just divide the whole thing by two and therefore be left with - 1 ± square root of 6, but this gives me a different answer. So, my question is, when do I reduce and are there rules to it?

I normally divide also. In this case, your text did not simplify, which is not standard practice. Simplify when you can.

When working with the quadratic formula, it's important to understand when and why simplification is acceptable. In general, simplification can be done if the simplified form preserves the important information and properties of the expression, such as the signs of the terms and the presence of any square roots.

In the case of the quadratic formula, let's start with the general form:

x = (-b ± √(b^2 - 4ac)) / (2a)

When you got the result (-2 ± 2√6) / 2, you actually have a common factor of 2 in the numerator. So, you can simplify the expression further by dividing both terms in the numerator by 2. Doing this gives you:

(-2/2 ± 2√6/2) = -1 ± √6

So both expressions: (-2 ± 2√6) / 2 and -1 ± √6 are equivalent, but the second one is the simplified form.

However, sometimes simplifying may not be appropriate. This typically occurs when there are additional mathematical operations or relationships involved, and reducing the expression would cause a loss of information. For example, if you were solving a problem where you needed to differentiate between the two solutions given by -1 ± √6, and simplifying to -1 ± √6 would not differentiate between them effectively, then it may be more appropriate to leave it in its original form.

In summary, when using the quadratic formula, simplification can be done as long as it doesn't alter the important aspects of the expression, such as the sign or presence of square roots. It is important to consider the context of the problem and whether simplification may result in a loss of information.