// Numbas version: finer_feedback_settings
{"name": "Considering efficiency - roots of a quartic real polynomial", "extensions": [], "custom_part_types": [], "resources": [["question-resources/wm175_method_1.png", "/srv/numbas/media/question-resources/wm175_method_1.png"], ["question-resources/20210608_165320.jpg", "/srv/numbas/media/question-resources/20210608_165320.jpg"], ["question-resources/wm175_method_1_jNN3Dz7.png", "/srv/numbas/media/question-resources/wm175_method_1_jNN3Dz7.png"], ["question-resources/method_1.jpg", "/srv/numbas/media/question-resources/method_1.jpg"], ["question-resources/method_2.jpg", "/srv/numbas/media/question-resources/method_2.jpg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Considering efficiency - roots of a quartic real polynomial", "tags": [], "metadata": {"description": "<p>Given two complex numbers, find by inspection the one that is a root of a given quartic real polynomial and hence find the other roots.&nbsp;</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Consider both methods shown to get the correct answer to the question below.<br/>After looking through both methods, choose which one you prefer and say why, giving a full explanation of your choice.</p>\n<p>Remember to compare efficiency, clarity of setting out, the reader's ability to follow the logic used easily in your answer.<br/><br/><strong>Question</strong></p>\n<p>Given &nbsp;$\\displaystyle f(z) = \\simplify[std]{z ^ 4+ 4*z ^ 3+ 28 * z^2 +240z+800}$, one of the following complex numbers is a root $z_1$ of the equation $f(z)=0$.</p>\n<p>Choose the correct value for $z_1$:&nbsp; &nbsp; &nbsp;(i)&nbsp; $1-4i$ &nbsp; &nbsp; &nbsp;or&nbsp; &nbsp; &nbsp;(ii)&nbsp; $-4+2i$</p>\n<p><br/><img src=\"resources/question-resources/method_1.jpg\" width=\"545\" height=\"726\"/>&nbsp; &nbsp; <img src=\"resources/question-resources/method_2.jpg\" width=\"543\" height=\"725\"/></p>\n<p></p>\n<p></p>\n<p><span style=\"text-decoration: underline;\"></span></p>", "advice": "<p></p>\n<p>&nbsp;</p>", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {"ch": {"parameters": [["a", "number"], ["s", "number"], ["b", "number"], ["r", "number"], ["t", "number"]], "type": "number", "language": "jme", "definition": "if(round(a^2+b^2)|round(s),ch(a,s,random(r..t except 0),r,t),b)"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Please give your full reasoning for which of the methods shown above you prefer.<br/><br/></p>\n<p>You should aim to write about 50 words in your answer.</p>\n<p>Then send it to Shaheen Charlwood via Teams direct chat before the submission time given (usually the end time of the exam).</p>\n<p></p>", "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Shaheen Charlwood", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1809/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Shaheen Charlwood", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1809/"}]}