El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\frac{\left(4 x^{2} + 4 x\right) + 1}{2 x + 4} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = - \frac{1}{2}$$
Solución numérica$$x_{1} = -0.499999285468973$$
$$x_{2} = -0.499999328563203$$
$$x_{3} = -0.499999276782946$$
$$x_{4} = -0.499999323666169$$
$$x_{5} = -0.499999297773473$$
$$x_{6} = -0.499999321705348$$
$$x_{7} = -0.499999396383697$$
$$x_{8} = -0.499999413128907$$
$$x_{9} = -0.499999322134376$$
$$x_{10} = -0.499999362643848$$
$$x_{11} = -0.499999293535667$$
$$x_{12} = -0.499999335895364$$
$$x_{13} = -0.499999324608462$$
$$x_{14} = -0.499999560357178$$
$$x_{15} = -0.499999348080144$$
$$x_{16} = -0.499999368290562$$
$$x_{17} = -0.499999330465674$$
$$x_{18} = -0.499999246202146$$
$$x_{19} = -0.49999932801067$$
$$x_{20} = -0.499999292896166$$
$$x_{21} = -0.49999932570747$$
$$x_{22} = -0.499999322362559$$
$$x_{23} = -0.499999331986873$$
$$x_{24} = -0.49999926807421$$
$$x_{25} = -0.499999299633838$$
$$x_{26} = -0.499999326547644$$
$$x_{27} = -0.49999932427869$$
$$x_{28} = -0.499999327492588$$
$$x_{29} = -0.499999042597831$$
$$x_{30} = -0.499999286707988$$
$$x_{31} = -0.499999296603569$$
$$x_{32} = -0.499999323381237$$
$$x_{33} = -0.499999298455727$$
$$x_{34} = -0.499999224185269$$
$$x_{35} = -0.49999926410815$$
$$x_{36} = -0.499999375335709$$
$$x_{37} = -0.49999927142642$$
$$x_{38} = -0.499999324955556$$
$$x_{39} = -0.499999332842245$$
$$x_{40} = -0.499999294132425$$
$$x_{41} = -0.499999339961871$$
$$x_{42} = -0.499999321503433$$
$$x_{43} = -0.499999179709007$$
$$x_{44} = -0.499999206466141$$
$$x_{45} = -0.499999297015249$$
$$x_{46} = -0.499999298123364$$
$$x_{47} = -0.499999287833966$$
$$x_{48} = -0.499999280873309$$
$$x_{49} = -0.499999329153741$$
$$x_{50} = -0.499999297404629$$
$$x_{51} = -0.499999331197106$$
$$x_{52} = -0.499999291469144$$
$$x_{53} = -0.499999253508824$$
$$x_{54} = -0.499999298771847$$
$$x_{55} = -0.499999345646721$$
$$x_{56} = -0.499999296167618$$
$$x_{57} = -0.499999274297059$$
$$x_{58} = -0.499999326115581$$
$$x_{59} = -0.499999438094521$$
$$x_{60} = -0.499999325321373$$
$$x_{61} = -0.499999299359896$$
$$x_{62} = -0.49999935415601$$
$$x_{63} = -0.499999323964973$$
$$x_{64} = -0.499999294690585$$
$$x_{65} = -0.499999295705183$$
$$x_{66} = -0.499999384372262$$
$$x_{67} = -0.499999236784193$$
$$x_{68} = -0.499999300385607$$
$$x_{69} = -0.499999300145931$$
$$x_{70} = -0.499999322600648$$
$$x_{71} = -0.499999299895584$$
$$x_{72} = -0.499999341634885$$
$$x_{73} = -0.499999292209157$$
$$x_{74} = -0.499999278956577$$
$$x_{75} = -0.499999322849299$$
$$x_{76} = -0.499999479309901$$
$$x_{77} = -0.499999327005832$$
$$x_{78} = -0.499999288861701$$
$$x_{79} = -0.499999290669745$$
$$x_{80} = -0.499999282576146$$
$$x_{81} = -0.499999295213776$$
$$x_{82} = -0.499999323109234$$
$$x_{83} = -0.499999284099$$
$$x_{84} = -0.499999289803512$$
$$x_{85} = -0.499999321915491$$
$$x_{86} = -0.499999333771749$$
$$x_{87} = -0.499999329786344$$
$$x_{88} = -0.499999259342632$$
$$x_{89} = -0.499999796388364$$
$$x_{90} = -0.499999299072885$$
$$x_{91} = -0.49999930061528$$
$$x_{92} = -0.499999358016769$$
$$x_{93} = -0.499999337115833$$
$$x_{94} = -0.49999913462949$$
$$x_{95} = -0.499999300835564$$
$$x_{96} = -0.49999934351603$$
$$x_{97} = -0.49999933478546$$
$$x_{98} = -0.499999350885753$$
$$x_{99} = -0.499999338464257$$