// Numbas version: finer_feedback_settings
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"rulesets": {}, "extensions": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Desarrollo", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Para determinar la naturaleza de las soluciones de una ecuaci&oacute;n de segundo grado de la forma $ax^2+bx+c=0$, debemos determinar su discriminante $\\triangle$, cuya f&oacute;rmula esta dada por la expresi&oacute;n $\\triangle=b^2-4 \\cdot a \\cdot c$.</p>\n<p>Recordemos que seg&uacute;n los siguientes valores de&nbsp;$\\triangle$, se obtienen la naturaleza de las soluciones:</p>\n<table border=\"1\" style=\"margin-left: auto; margin-right: auto;\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\">Condici&oacute;n</td>\n<td style=\"text-align: center;\">Valor</td>\n<td style=\"text-align: center;\">Naturaleza</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">$\\triangle&gt;0$</td>\n<td style=\"text-align: center;\">Positivo</td>\n<td style=\"text-align: center;\">Reales y Distintas</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">$\\triangle=0$</td>\n<td style=\"text-align: center;\">0</td>\n<td style=\"text-align: center;\">Reales e Iguales</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">$\\triangle&lt;0$</td>\n<td style=\"text-align: center;\">Negativo</td>\n<td style=\"text-align: center;\">Complejas y Conjugadas</td>\n</tr>\n</tbody>\n</table>\n<hr/>\n<p>An&aacute;lisis de i)&nbsp;$2x^2-3x+1=0$.</p>\n<p>Los valores de $a$, $b$ y $c$ son $a=$[[0]], $b=$[[1]] y $c=$[[2]].&nbsp;</p>\n<p>El discriminante de esta ecuaci&oacute;n es:</p>\n<p style=\"text-align: center;\">$\\triangle=$ $($&nbsp;[[1]] $)$$^2$ $-4 \\cdot$&nbsp;[[0]]&nbsp;$\\cdot$[[2]]</p>\n<p style=\"text-align: center;\">$\\triangle=$&nbsp;[[3]]&nbsp;[[4]]&nbsp;[[5]]</p>\n<p style=\"text-align: center;\">$\\triangle=$[[6]]</p>\n<p style=\"text-align: left;\">Para esta ecuaci&oacute;n el&nbsp;$\\triangle=$ es&nbsp;[[7]], por tanto las soluciones son&nbsp;[[8]].</p>\n<hr/>\n<p style=\"text-align: left;\">An&aacute;lisis de i) $4x^2+6x-5=0$.</p>\n<p>Los valores de $a$, $b$ y $c$ son $a=$[[9]], $b=$[[10]]&nbsp;y $c=$[[11]].&nbsp;</p>\n<p>El discriminante de esta ecuaci&oacute;n es:</p>\n<p style=\"text-align: center;\">$\\triangle=$ $($&nbsp;[[10]]&nbsp;$)$$^2$ $-4 \\cdot$&nbsp;[[9]]&nbsp;$\\cdot$[[11]]</p>\n<p style=\"text-align: center;\">$\\triangle=$&nbsp;[[12]]&nbsp;[[13]]&nbsp;[[14]]</p>\n<p style=\"text-align: center;\">$\\triangle=$[[15]]</p>\n<p style=\"text-align: left;\">Para esta ecuaci&oacute;n el&nbsp;$\\triangle=$ 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