Algebraic expressions

1) Non-negative values a and b satasfyed a+b=0. Find the values of a and b.

2) Factor:
(x^2-2x)^2-2(x^2-2x)-3

Question

Algebraic expressions

1) Non-negative values a and b satasfyed a+b=0. Find the values of a and b.

2) Factor:
(x^2-2x)^2-2(x^2-2x)-3

accessdenied · Answer

1)  a + b = 0
If we solve this for one value
a = -b
If we make one positive, the other $has$ to be negative.  So I believe we only have one possible solution.  Can you see it?

2)  We should treat this as if  w = x^2 - 2x:   w^2 - 2w - 3 .  Are you able to factor this quadratic?

accessdenied · Answer

And for #1 we should distinguish between non-negative and positive.  They're not quite synonymous, because there is one number between positives and negatives that is non-negative but not positive.

anonymous · Answer

I dont really know what you mean by one number thats not negitive and not positive, it can only be a decimal right, but it also can be a decimal because itwont equal to 0

accessdenied · Answer

0 itself is neither positive nor negative.
Even though it doesn't have a negative sign, it has no magnitude in the positive direction either.  It is in between positive and negatives.

anonymous · Answer

Can't^

accessdenied · Answer

If you think about the positive numbers with negative numbers as their inverses for addition, and,
  a + -a = 0
For 0, what is its inverse?
  0 + ? = 0
Well, 0.
  0 + 0 = 0,  0 - 0 = 0     0 is its own inverse.

accessdenied · Answer

But it wouldn't make sense to call 0 both positive and negative, the groups are different.
So 0 is neither positive nor negative.  Does that make sense?

accessdenied · Answer

But then one more step ahead,
non-negative means "not negative"
the positives are not negative, that is true.
zero, being neither positive nor negative, is ALSO not negative!  :)