Question 233174: I really need help on learning how to use the Zero Product Property to solve problems like n^2+7n+6=0 ive had the flu so now im having to do all my make up work before i go back to school and i wasnt there for this lesson and i dont understand it all! Please help me.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! your answer is here:
Zero Product Property
You can thank Colleen
Basically, if a * b = 0, then either a = 0 or b = 0 or both.
Your problem is:
n^2+7n+6=0
This can be factored to become:
(n+6) * (n+1) = 0
This means that either (n+6) must equal zero, or (n+1) must equal 0.
If n+6 = 0, this means that n = -6
If n+1 = 0, this means that n = -1
Your answer is that n = -6 or n = -1
You then test these solutions in your original equation to see if they are true.
If n = -1, then n^2 + 7n + 6 = becomes (-1)^2 + 7*(-1) + 6 = 0 becomes 1 - 7 + 6 = 0 becomes 0 = 0.
Since the equation is true, n = -1 is a good answer.
If n = -6, then n^2 + 7n + 6 becomes (-6)^2 + 7(-6) + 6 = 0 becomes 36 - 42 + 6 = 0 becomes -6 + 6 = 0 becomes 0 = 0.
Since the equaion is true, n = -6 is a good answer also.
Your answer is that n can be either -1 or -6 as long as there are no restrictions on whether n can be negative or not. That depends on what n represents. In this particular problem, it doesn't represent anything that can't be negative so your answer is valid.
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