SOLUTION: Hello, I'm just a little confused by what the following question is asking: What two numbers are represented by each of the following? 1. -6 plus or minus (sqrt 6) I think it

Question 452709: Hello,
I'm just a little confused by what the following question is asking:
What two numbers are represented by each of the following?
1. -6 plus or minus (sqrt 6) I think it is asking for the answer of -6 + (sqrt 6) and -6 - (sqrt 6) since nothing can be factored out of (sqrt 6).
2. 4/3 plus or minus (i sqrt 2) /3 I think the answers would be (4+ (isqrt2))/3 and ((4 - (i sqrt 2))/3
but it could be 1 + ((1+isqrt2))/3 and 1 - ((1+isqrt2))/3
and the next question:
what must be added to make the given expression a trinomial square?
m^2 - 4m + ? I think the answer is 4, if the equation were factored it would be (m-2)(m-2)
a^2 + 12a + ? not sure how to do this equation however.

please show me how to correctly do these equations. Thank you
Answer by ilana(307) (Show Source): You can put this solution on YOUR website!
1. I think you are correct.
2. I think your first choice is correct.
These seem to just want you to know the meaning of "plus or minus".
3. You are correct, 4 is the answer.
4. Look at what you did for #3. You took the coefficient of m and divided it by 2, and then squared it. (-4/2 = -2, and (-2)^2 = 4.) This comes from the fact that (a + b)^2 = a^2 + 2ab + b^2. So in this case, for #4, divide 12 by 2 (and get 6), and then square that (and get 36). So the answer is 36. The factored expression would be (a + 6)(a + 6).
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