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Decimal expansion of the x nearest 0 that satisfies x^2+4x+3=e^x.
4

%I #5 Mar 30 2012 18:58:03

%S 7,9,5,2,2,6,6,1,3,8,6,0,5,4,0,7,9,8,8,9,6,2,6,1,5,5,6,3,8,8,7,1,8,0,

%T 2,9,3,6,3,7,4,8,5,3,8,5,6,2,0,8,7,8,6,0,3,5,7,5,0,0,6,4,4,0,0,6,9,4,

%U 8,1,6,2,4,2,3,4,8,1,2,6,8,5,9,0,8,7,3,9,7,0,2,5,4,6,5,0,8,1,3

%N Decimal expansion of the x nearest 0 that satisfies x^2+4x+3=e^x.

%C See A201741 for a guide to related sequences. The Mathematica program includes a graph.

%e least: -3.024014501135293784775589627797395351659...

%e nearest to 0: -0.79522661386054079889626155638871...

%e greatest: 3.2986275628038651802559413164923413431...

%t a = 1; b = 4; c = 3;

%t f[x_] := a*x^2 + b*x + c; g[x_] := E^x

%t Plot[{f[x], g[x]}, {x, -3.5, 3.5}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, -3.1, -3.0}, WorkingPrecision -> 110]

%t RealDigits[r] (* A201924 *)

%t r = x /. FindRoot[f[x] == g[x], {x, -.8, -.7}, WorkingPrecision -> 110]

%t RealDigits[r] (* A201925 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 3.2, 3.3}, WorkingPrecision -> 110]

%t RealDigits[r] (* A201926 *)

%Y Cf. A201741.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Dec 06 2011