SOLUTION: Find the value of a,b, or c so that each equation will have exactly one rational solution. p^2+bp+25=0

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Question 888797: Find the value of a,b, or c so that each equation will have exactly one rational solution. p^2+bp+25=0

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
p^2+10p+25=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ap%5E2%2Bbp%2Bc=0 (in our case 1p%5E2%2B10p%2B25+=+0) has the following solutons:

p%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=%2810%29%5E2-4%2A1%2A25=0.

Discriminant d=0 is zero! That means that there is only one solution: p+=+%28-%2810%29%29%2F2%5C1.
Expression can be factored: 1p%5E2%2B10p%2B25+=+1%28p--5%29%2A%28p--5%29

Again, the answer is: -5, -5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B10%2Ax%2B25+%29