SOLUTION: The directions say to solve each equation by graphing. The problem is written as; {{{5n^2+2n+6 = 0}}}

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: The directions say to solve each equation by graphing. The problem is written as; {{{5n^2+2n+6 = 0}}}      Log On


   

Question 180288This question is from textbook Algebra I
: The directions say to solve each equation by graphing.
The problem is written as;
5n%5E2%2B2n%2B6+=+0 This question is from textbook Algebra I

Found 2 solutions by stanbon, Mathtut:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
5n^2+2n+6 = 0
graph%28400%2C300%2C-10%2C10%2C-10%2C20%2C5x%5E2%2B2x%2B6%29
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Notice the graph does not cross the x-axis so there are no Real Number solutions.
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You would have to use the Quadratic formula to find the Complex
Number solutions.
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Cheers,
Stan H.

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
this quadratic produces complex roots
:
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B2x%2B6+=+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=%282%29%5E2-4%2A5%2A6=-116.

The discriminant -116 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -116 is + or - sqrt%28+116%29+=+10.770329614269.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B2%2Ax%2B6+%29