SOLUTION: Hi would you please help me solve my homework problem. Find the value of a so that the equation below will have exactly one rational solution. use quadratic formula am^2+8m+

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Question 921394: Hi would you please help me solve my homework problem.
Find the value of a so that the equation below will have exactly one rational solution. use quadratic formula
am^2+8m+1=0
My teacher said that the answer is a=16. Would you please show me the steps on how to solve this problem. Thank you.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
am^2+8m+1 or ax^2+8x+1 is in the form ax^2 + bx + c

a is unknown
b = 8
c = 1


The discriminant formula D+=+b%5E2+-+4ac will help answer this problem. When D+=+0, we'll have exactly one rational solution.


D+=+b%5E2+-+4ac


D+=+8%5E2+-+4%2Aa%2A1 Plug in b = 8 and c = 1


D+=+64+-+4a


0+=+64+-+4a Plug in D = 0 because we want exactly one rational solution.


4a+=+64


a+=+64%2F4


a+=+16


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