SOLUTION: A student opens a mathematics book to 2 facing pages. The product of the page numbers is 1806. Find the page numbers. The first page number is The second page number is

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: A student opens a mathematics book to 2 facing pages. The product of the page numbers is 1806. Find the page numbers. The first page number is The second page number is       Log On


   

Question 182692: A student opens a mathematics book to 2 facing pages. The product of the page numbers is 1806. Find the page numbers. The first page number is
The second page number is
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
lets call the 2 consecutive pages a and b......but we know that b=a+1
:
a(a+1)=1806
:
a^2+a-1806=0
:
there arent negative page numbers so throw out -43
:
a=highlight%2842%29
:
b=a%2B1=highlight%2843%29
:
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B1x%2B-1806+=+0) has the following solutons:

x%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=%281%29%5E2-4%2A1%2A-1806=7225.

Discriminant d=7225 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+7225+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281%29%2Bsqrt%28+7225+%29%29%2F2%5C1+=+42
x%5B2%5D+=+%28-%281%29-sqrt%28+7225+%29%29%2F2%5C1+=+-43

Quadratic expression 1x%5E2%2B1x%2B-1806 can be factored:
1x%5E2%2B1x%2B-1806+=+%28x-42%29%2A%28x--43%29
Again, the answer is: 42, -43. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B-1806+%29