// Numbas version: finer_feedback_settings
{"name": "Harder practice Q - roots of a cubic ", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Harder practice Q - roots of a cubic ", "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Using either algebraic division or the factor theorem, choose which one of these complex numbers is a root of the given equation $f(z)=0$ , and hence find all the roots.</p>", "advice": "", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"s1": {"name": "s1", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "templateType": "anything", "can_override": 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variables", "definition": "s1*random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "c2": {"name": "c2", "group": "Ungrouped variables", "definition": "s6*random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "x1a1": {"name": "x1a1", "group": "Ungrouped variables", "definition": "if(tx1a1=a1,a1+1,tx1a1)", "description": "", "templateType": "anything", "can_override": false}, "x2a1": {"name": "x2a1", "group": "Ungrouped variables", "definition": "if(tx2a1=a1,a1+1,tx2a1)", "description": "", "templateType": "anything", "can_override": false}, "tx1a1": {"name": "tx1a1", "group": "Ungrouped variables", "definition": "s1*random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "z3": {"name": "z3", "group": "Ungrouped variables", "definition": "x2a1+x2b1*i", "description": "", "templateType": "anything", "can_override": false}, "x2b2": {"name": "x2b2", "group": "Ungrouped variables", "definition": "xs3*random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "xs2": {"name": "xs2", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "templateType": "anything", "can_override": false}, "a2": {"name": "a2", "group": "Ungrouped variables", "definition": "s4*random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "x1a2": {"name": "x1a2", "group": "Ungrouped variables", "definition": "if(tx1a2=a2,a2+1,tx1a2)", "description": "", "templateType": "anything", "can_override": false}, "tx3a2": {"name": "tx3a2", "group": "Ungrouped variables", "definition": "s6*random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "z1": {"name": "z1", "group": "Ungrouped variables", "definition": "a1+ b1*i", "description": "", "templateType": "anything", "can_override": false}, "tx1a2": {"name": "tx1a2", "group": "Ungrouped variables", "definition": "s3*random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "tx2a1": {"name": "tx2a1", "group": "Ungrouped variables", "definition": "s3*random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "b1": {"name": "b1", "group": "Ungrouped variables", "definition": "if(abs(a1)=f1,f1+1,f1)", "description": "", "templateType": "anything", "can_override": false}, "z4": {"name": "z4", "group": "Ungrouped variables", "definition": "x3a1+x3b1*i", "description": "", "templateType": "anything", "can_override": false}, "x1b2": {"name": "x1b2", "group": "Ungrouped variables", "definition": "xs2*random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "z2": {"name": "z2", "group": "Ungrouped variables", "definition": "x1a1+x1b1*i", "description": "", "templateType": "anything", "can_override": false}, "b2": {"name": "b2", "group": "Ungrouped variables", "definition": "s5*random(1..9)", "description": "", "templateType": "anything", "can_override": 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"ungrouped_variables": ["tx3a1", "f1", "tx3a2", "b2", "tx2a2", "x1b2", "x1b1", "b1", "tx1a1", "tx2a1", "xs2", "xs3", "xs1", "x3a1", "x3a2", "s3", "s2", "s1", "s6", "s5", "s4", "x2a1", "x2a2", "x1a2", "x1a1", "a1", "a2", "z4", "c2", "c1", "z1", "z2", "z3", "x3b1", "x3b2", "x2b1", "x2b2", "tx1a2"], "variable_groups": [], "functions": {}, "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>Given &nbsp;$\\displaystyle f(z) = \\simplify[std]{z ^ 3 + {( -2) * a1 -c1}*z ^ 2 + {2 * a1 * c1 + a1 ^ 2 + b1 ^ 2} * z -{c1 * (a1 ^ 2 + b1 ^ 2)}}$, one of the following complex numbers is a root $z_1$ 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[]}], "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/"}]}