SOLUTION: Please explain and factor the polynomial: n^2/4 - 9/16

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Question 5292: Please explain and factor the polynomial:
n^2/4 - 9/16
Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
all you have to do is solve equation n%5E2%2F4=9%2F16=0
and then use the standard formula of factoring the trinomial, given its roots.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation an%5E2%2Bbn%2Bc=0 (in our case 0.25n%5E2%2B0n%2B-0.5625+=+0) has the following solutons:

n%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%280%29%5E2-4%2A0.25%2A-0.5625=0.5625.

Discriminant d=0.5625 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-0%2B-sqrt%28+0.5625+%29%29%2F2%5Ca.

n%5B1%5D+=+%28-%280%29%2Bsqrt%28+0.5625+%29%29%2F2%5C0.25+=+1.5
n%5B2%5D+=+%28-%280%29-sqrt%28+0.5625+%29%29%2F2%5C0.25+=+-1.5

Quadratic expression 0.25n%5E2%2B0n%2B-0.5625 can be factored:
0.25n%5E2%2B0n%2B-0.5625+=+0.25%28n-1.5%29%2A%28n--1.5%29
Again, the answer is: 1.5, -1.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+0.25%2Ax%5E2%2B0%2Ax%2B-0.5625+%29