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A201925 Decimal expansion of the x nearest 0 that satisfies x^2+4x+3=e^x.

%I A201925 #8 Feb 07 2025 16:44:07
%S A201925 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 A201925 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 A201925 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 A201925 Decimal expansion of the x nearest 0 that satisfies x^2+4x+3=e^x.
%C A201925 See A201741 for a guide to related sequences. The Mathematica program includes a graph.
%H A201925 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201925 least:  -3.024014501135293784775589627797395351659...
%e A201925 nearest to 0:  -0.79522661386054079889626155638871...
%e A201925 greatest:  3.2986275628038651802559413164923413431...
%t A201925 a = 1; b = 4; c = 3;
%t A201925 f[x_] := a*x^2 + b*x + c; g[x_] := E^x
%t A201925 Plot[{f[x], g[x]}, {x, -3.5, 3.5}, {AxesOrigin -> {0, 0}}]
%t A201925 r = x /. FindRoot[f[x] == g[x], {x, -3.1, -3.0}, WorkingPrecision -> 110]
%t A201925 RealDigits[r]     (* A201924 *)
%t A201925 r = x /. FindRoot[f[x] == g[x], {x, -.8, -.7}, WorkingPrecision -> 110]
%t A201925 RealDigits[r]     (* A201925 *)
%t A201925  r = x /. FindRoot[f[x] == g[x], {x, 3.2, 3.3}, WorkingPrecision -> 110]
%t A201925 RealDigits[r]     (* A201926 *)
%Y A201925 Cf. A201741.
%K A201925 nonn,cons
%O A201925 0,1
%A A201925 _Clark Kimberling_, Dec 06 2011