// Numbas version: finer_feedback_settings
{"name": "Pregunta 6: Ecuaciones de Segundo Grado", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Pregunta 6: Ecuaciones de Segundo Grado", "tags": [], "metadata": {"description": "<p>Objetivo: Determinar las soluciones de una ecuaci&oacute;n de segundo grado usando la f&oacute;rmula general&nbsp;$x= \\Large\\frac{-b \\pm \\sqrt{b^2-4 \\cdot a \\cdot c}}{2 \\cdot a}$</p>", "licence": "None specified"}, "statement": "<p>6)&nbsp;&nbsp;Determine las ra&iacute;ces de la ecuaci&oacute;n de segundo grado $10x^2+5x-5=0$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;</p>", "advice": "", "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 las soluciones de una ecuaci&oacute;n de segundo grado de la forma $ax^2+bx+c=0$, usaremos la f&oacute;rmula general de las soluciones la cual es $x= \\Large\\frac{-b \\pm \\sqrt{b^2-4 \\cdot a \\cdot c}}{2 \\cdot a}$.</p>\n<table style=\"width: 893px;\" border=\"1\">\n<tbody>\n<tr style=\"height: 55px;\">\n<td style=\"width: 435px; text-align: center; height: 55px;\">$10x^2+5x-5=0$</td>\n<td style=\"width: 445px; text-align: left; height: 55px;\"><strong>Paso 1:</strong>&nbsp;Primero debemos determinar los valores de $a$, $b$ y $c$ en la ecuaci&oacute;n&nbsp;$10x^2+5x-5=0$, obteniendo que estos valores son $a=$[[0]],&nbsp; &nbsp; $b=$[[1]]&nbsp; y&nbsp; &nbsp; &nbsp; $c=$[[2]].</td>\n</tr>\n<tr style=\"height: 155px;\">\n<td style=\"width: 435px; text-align: center; height: 155px;\">\n<p>$($[[1]]$)$$^2$$-4 \\cdot$&nbsp;[[0]] $\\cdot$[[2]]</p>\n<p>[[3]][[5]][[4]]</p>\n<p>[[6]]</p>\n</td>\n<td style=\"width: 445px; height: 155px;\">\n<p style=\"text-align: left;\"><strong>Paso 2:&nbsp;</strong>Vamos a determinar el valor de la expresi&oacute;n $b^2-4ac$.</p>\n<p style=\"text-align: left;\">&nbsp;-&nbsp; Calculamos $b^2$</p>\n<p style=\"text-align: left;\">&nbsp;-&nbsp; Determinamos el valor de $-4ac$ y su signo</p>\n<p style=\"text-align: left;\">&nbsp;-&nbsp; Reducimos&nbsp;los valores anteriores</p>\n</td>\n</tr>\n<tr style=\"height: 34px;\">\n<td style=\"width: 435px; text-align: center; height: 34px;\">[[7]]</td>\n<td style=\"width: 445px; height: 34px; text-align: left;\"><strong>Paso 3:&nbsp;</strong>Sacamos la ra&iacute;z cuadrada del valor obtenido al final del <strong>paso 2</strong>, para as&iacute; obtener cuanto vale $\\sqrt{b^2-4ac}$.</td>\n</tr>\n<tr style=\"height: 24px;\">\n<td style=\"width: 435px; height: 24px; text-align: left;\"><strong>Paso 4:&nbsp;</strong> Reemplazamos el valor del <strong>paso 3&nbsp;</strong>en la formula general obteniendo as&iacute; las dos soluciones pedidas:</td>\n<td style=\"width: 445px; height: 24px; text-align: left;\"><strong>Observaci&oacute;n:</strong> Como ya sabemos que $\\sqrt{b^2-4ac}=$[[7]], entonces ahora reemplazamos en:</td>\n</tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 435px; height: 17px; text-align: center;\">\n<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;$-$[[1]]$+$[[7]]</p>\n<p>$x_1=$ _________________</p>\n<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;$2\\cdot$[[0]]&nbsp;</p>\n<p style=\"text-align: left;\"><strong>Paso 5:&nbsp;</strong>Ahora debes desarrollar el numerador y denominador obteniendo:</p>\n</td>\n<td style=\"width: 445px; height: 17px;\">\n<p style=\"text-align: center;\">&nbsp; &nbsp; &nbsp; &nbsp;$-$[[1]]$-$[[7]]</p>\n<p style=\"text-align: center;\">$x_2=$ _________________</p>\n<p style=\"text-align: center;\">&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;$2\\cdot$[[0]]&nbsp;</p>\n<p style=\"text-align: left;\"><strong>Paso 5:&nbsp;</strong>Ahora debes desarrollar el numerador y denominador obteniendo:</p>\n</td>\n</tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 435px; height: 17px; text-align: center;\">\n<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;[[8]]</p>\n<p>$x_1=$ _______</p>\n<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;[[10]]</p>\n</td>\n<td style=\"width: 445px; height: 17px; text-align: center;\">\n<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;[[9]]</p>\n<p>$x_2=$ _______</p>\n<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;[[10]]</p>\n</td>\n</tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 435px; height: 17px; text-align: left;\"><strong>Paso 6:&nbsp;</strong>Simplificar las fracciones obtenidas en el paso 5, dejarla como entero en caso de serlo, y si es decimal dejarlo escrito con una sola cifra decimal</td>\n<td style=\"width: 445px; height: 17px;\"><strong>Paso 6:&nbsp;</strong>Simplificar las fracciones obtenidas en el paso 5, dejarla como entero en caso de serlo, y si es decimal dejarlo escrito con una sola cifra decimal</td>\n</tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 435px; height: 17px; text-align: center;\">$x_1=$[[11]]</td>\n<td style=\"width: 445px; height: 17px; text-align: center;\">\n<p>$x_2=$[[12]]</p>\n</td>\n</tr>\n</tbody>\n</table>\n<p>&nbsp; &nbsp;&nbsp;</p>\n<p></p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "10", "maxValue": "10", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "5", "maxValue": "5", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "-5", "maxValue": "-5", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "25", "maxValue": "25", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "200", "maxValue": "200", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["+", "-"], "matrix": ["0.2", 0], "distractors": ["", ""]}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "225", "maxValue": "225", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "15", "maxValue": "15", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.25", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "10", "maxValue": "10", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.25", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "-20", "maxValue": "-20", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "20", "maxValue": "20", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.5", "maxValue": "0.5", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "-1", "maxValue": "-1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Emilio Gonz\u00e1lez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/9326/"}]}]}], "contributors": [{"name": "Emilio Gonz\u00e1lez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/9326/"}]}