SOLUTION: Determine the number of real number solutions to the equation from this given graph. 5x2 + 4x + 6 = 0, given the graph of y = 5x2 + 4x + 6

Algebra ->  Linear-equations -> SOLUTION: Determine the number of real number solutions to the equation from this given graph. 5x2 + 4x + 6 = 0, given the graph of y = 5x2 + 4x + 6      Log On


   

Question 405010: Determine the number of real number solutions to the equation from this given graph.
5x2 + 4x + 6 = 0, given the graph of y = 5x2 + 4x + 6
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Here is the graph of :

+y+=+5x%5E2+%2B+4x+%2B+6

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+5x%5E2+%2B+4x+%2B+6%29+


Notice that the equation 5x%5E2+%2B+4x+%2B+6 can be written as 0+=+5x%5E2+%2B+4x+%2B+6 which amounts to replacing y in y+=+5x%5E2+%2B+4x+%2B+6 by 0.

So we really have this system:
system%28y+=+5x%5E2+%2B+4x+%2B+6%2Cy=0%29
And y=0 is the equation of the x-axis.
Therefore we look to see what+points if any the graph of y+=+45x%5E2+%2B+4x+%2B+6 has in common with the x-axis.
It appears that there is no point the curve has in common with the x-axis and it is not a tangent to the x-axis anywhere.
So the equation 5x%5E2+%2B+4x+%2B+6 appears to have no real number solution.