+1791 I need help with quadratic equations!!
The quadratic equation $x^2+4mx+m = 2x - 6$ has exactly one real root. Find the positive value of $m$.
+128707 Rearrange as x^2 + (4m -2) + (m + 6) = 0
If we have one real root....the discriminant = 0
So
(4m - 2)^2 - 4 (1) ( m + 6) = 0
16m^2 - 16m + 4 - 4m - 24 = 0
16m^2 - 20m - 20 = 0 divide through by 4
4m^2 - 5m - 5 = 0
m = [ 5 + sqrt [ 25 - 4 (4)(-5) ] ] / (2 * 4 ) = [ 5 + sqrt ( 105) ] / 8
