SOLUTION: Find all values of c such that the equation 39 x2 + 49 x + c = 0 has exactly one solution.

Question 839785: Find all values of c such that the equation 39 x2 + 49 x + c = 0 has exactly one solution.
Answer by LinnW(1048) (Show Source): You can put this solution on YOUR website!
Consider the general form ax^2 + bx + c = 0
-b/2a gives the x value for the vertex.
For 39x^2 + 49x + c = 0 ,
-b/2a = -(49)/(2(39)) = -49/78
We want a value of c such that when -49/78 is substituted for x,
y = 0 in y = 39x^2 + 49x + c
39(-49/78)^2 + 49(-49/78) + c = 0
add -c to each side
39(-49/78)^2 + 49(-49/78) = -c
multiply each side by -1
-1(39(-49/78)^2 + 49(-49/78)) = -1(-c)
-1*(39*(-49/78)^2 + 49*(-49/78)) = c
So c = 2401/156 or 15 61/156
The following checks out
39(-49/78)^2 + 49(-49/78) +2401/156 = 0

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