{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":49967,"title":"When the sum of the cubes is a quartic...","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor a given value of n (i.e., num in the problem statement), determine the values of a's and b that satisfy the equality above. The answer should be put in a vector where the first \"num\" entries are the values of a's and the last entry is b. There is no unique answer to each of the problems; however, you answer will be checked against the requirement.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = cubes_quartic(num)\r\n  y = ones(num);\r\nend","test_suite":"%%\r\nnum=1;\r\ny=cubes_quartic(num);\r\naa=0;\r\nfor i=1:length(y)-1\r\n    aa=aa+y(i)^3;\r\nend\r\nassert(isequal(aa,y(end)^4))\r\n%%\r\nnum=2;\r\ny=cubes_quartic(num);\r\naa=0;\r\nfor i=1:length(y)-1\r\n    aa=aa+y(i)^3;\r\nend\r\nassert(isequal(aa,y(end)^4))\r\n%%\r\nnum=3;\r\ny=cubes_quartic(num);\r\naa=0;\r\nfor i=1:length(y)-1\r\n    aa=aa+y(i)^3;\r\nend\r\nassert(isequal(aa,y(end)^4))\r\n%%\r\nnum=4;\r\ny=cubes_quartic(num);\r\naa=0;\r\nfor i=1:length(y)-1\r\n    aa=aa+y(i)^3;\r\nend\r\nassert(isequal(aa,y(end)^4))\r\n%%\r\nnum=5;\r\ny=cubes_quartic(num);\r\naa=0;\r\nfor i=1:length(y)-1\r\n    aa=aa+y(i)^3;\r\nend\r\nassert(isequal(aa,y(end)^4))\r\n%%\r\nnum=6;\r\ny=cubes_quartic(num);\r\naa=0;\r\nfor i=1:length(y)-1\r\n    aa=aa+y(i)^3;\r\nend\r\nassert(isequal(aa,y(end)^4))\r\n%%\r\nnum=7;\r\ny=cubes_quartic(num);\r\naa=0;\r\nfor i=1:length(y)-1\r\n    aa=aa+y(i)^3;\r\nend\r\nassert(isequal(aa,y(end)^4))","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-01-23T22:34:54.000Z","updated_at":"2026-03-04T21:52:21.000Z","published_at":"2021-01-23T22:42:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider the following equality:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a given value of n (i.e., num in the problem statement), determine the values of a's and b that satisfy the equality above. 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version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the coefficients a, b, c, and d of a cubic equation, a*x^3 + b*x^2 + c*x + d = 0, determine its roots.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor a given value of n (i.e., num in the problem statement), determine the values of a's and b that satisfy the equality above. The answer should be put in a vector where the first \"num\" entries are the values of a's and the last entry is b. There is no unique answer to each of the problems; however, you answer will be checked against the requirement.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = cubes_quartic(num)\r\n  y = ones(num);\r\nend","test_suite":"%%\r\nnum=1;\r\ny=cubes_quartic(num);\r\naa=0;\r\nfor i=1:length(y)-1\r\n    aa=aa+y(i)^3;\r\nend\r\nassert(isequal(aa,y(end)^4))\r\n%%\r\nnum=2;\r\ny=cubes_quartic(num);\r\naa=0;\r\nfor i=1:length(y)-1\r\n    aa=aa+y(i)^3;\r\nend\r\nassert(isequal(aa,y(end)^4))\r\n%%\r\nnum=3;\r\ny=cubes_quartic(num);\r\naa=0;\r\nfor i=1:length(y)-1\r\n    aa=aa+y(i)^3;\r\nend\r\nassert(isequal(aa,y(end)^4))\r\n%%\r\nnum=4;\r\ny=cubes_quartic(num);\r\naa=0;\r\nfor i=1:length(y)-1\r\n    aa=aa+y(i)^3;\r\nend\r\nassert(isequal(aa,y(end)^4))\r\n%%\r\nnum=5;\r\ny=cubes_quartic(num);\r\naa=0;\r\nfor i=1:length(y)-1\r\n    aa=aa+y(i)^3;\r\nend\r\nassert(isequal(aa,y(end)^4))\r\n%%\r\nnum=6;\r\ny=cubes_quartic(num);\r\naa=0;\r\nfor i=1:length(y)-1\r\n    aa=aa+y(i)^3;\r\nend\r\nassert(isequal(aa,y(end)^4))\r\n%%\r\nnum=7;\r\ny=cubes_quartic(num);\r\naa=0;\r\nfor i=1:length(y)-1\r\n    aa=aa+y(i)^3;\r\nend\r\nassert(isequal(aa,y(end)^4))","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-01-23T22:34:54.000Z","updated_at":"2026-03-04T21:52:21.000Z","published_at":"2021-01-23T22:42:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider the following equality:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a given value of n (i.e., num in the problem statement), determine the values of a's and b that satisfy the equality above. 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the roots of a cubic equation","description":"Given the coefficients a, b, c, and d of a cubic equation, a*x^3 + b*x^2 + c*x + d = 0, determine its roots.","description_html":"\u003cp\u003eGiven the coefficients a, b, c, and d of a cubic equation, a*x^3 + b*x^2 + c*x + d = 0, determine its roots.\u003c/p\u003e","function_template":"function y = cubicRoots(a,b,c,d)\r\n  y = [0 0 0];\r\nend","test_suite":"%%\r\na=1; b=3; c=3; d=1;\r\ny_correct = [-1 -1 -1];\r\nassert(sum(abs(cubicRoots(a,b,c,d)-y_correct))\u003c1e-3)\r\n\r\n%%\r\na=1; b=-6; c=11; d=-6;\r\ny_correct = [1 2 3];\r\nassert(sum(abs(cubicRoots(a,b,c,d)-y_correct))\u003c1e-3)\r\n\r\n%%\r\na=4; b=4; c=-1; d=-1;\r\ny_correct = [-1 -0.5 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