[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki14\/2022\/03\/17\/%e9%87%8d%e6%a0%b9-%e5%a4%9a%e9%a0%85%e5%bc%8f-wikipedia\/#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki14\/2022\/03\/17\/%e9%87%8d%e6%a0%b9-%e5%a4%9a%e9%a0%85%e5%bc%8f-wikipedia\/","headline":"\u91cd\u6839 (\u591a\u9805\u5f0f) – Wikipedia","name":"\u91cd\u6839 (\u591a\u9805\u5f0f) – Wikipedia","description":"\u91cd\u6839\uff08\u3058\u3085\u3046\u3053\u3093\u3001\u82f1\u79f0\uff1amultiple root\uff09\u3068\u306f\u30011 \u5909\u6570\u591a\u9805\u5f0f f(x) \u306e\u6839\u306e\u3046\u3061\u91cd\u8907\u5ea6\u304c2\u4ee5\u4e0a\u306e\u3082\u306e\u306e\u3053\u3068\u3092\u3044\u3046\u3002 1 \u5909\u6570\u591a\u9805\u5f0f f(x) \u304c\u3001\u5b9a\u6570 a\u22600 ,\u03b11,\u03b12, \u2026 \u03b1n \u3092\u7528\u3044\u3066 f(x)=a(x\u2212\u03b11)(x\u2212\u03b12)\u22ef(x\u2212\u03b1n){displaystyle f(x)=a(x-alpha _{1})(x-alpha _{2})cdots (x-alpha _{n})}","datePublished":"2022-03-17","dateModified":"2022-03-17","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki14\/author\/lordneo\/#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki14\/author\/lordneo\/","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/19ab1ac9a6aee3d730e4506b46b6451d27b12cf5","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/19ab1ac9a6aee3d730e4506b46b6451d27b12cf5","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/jp\/wiki14\/2022\/03\/17\/%e9%87%8d%e6%a0%b9-%e5%a4%9a%e9%a0%85%e5%bc%8f-wikipedia\/","about":["Wiki"],"wordCount":1930,"articleBody":"\u91cd\u6839\uff08\u3058\u3085\u3046\u3053\u3093\u3001\u82f1\u79f0\uff1amultiple root\uff09\u3068\u306f\u30011 \u5909\u6570\u591a\u9805\u5f0f f(x) \u306e\u6839\u306e\u3046\u3061\u91cd\u8907\u5ea6\u304c2\u4ee5\u4e0a\u306e\u3082\u306e\u306e\u3053\u3068\u3092\u3044\u3046\u3002  1 \u5909\u6570\u591a\u9805\u5f0f f(x) \u304c\u3001\u5b9a\u6570 a\u22600 ,\u03b11,\u03b12, \u2026 \u03b1n \u3092\u7528\u3044\u3066f(x)=a(x\u2212\u03b11)(x\u2212\u03b12)\u22ef(x\u2212\u03b1n){displaystyle f(x)=a(x-alpha _{1})(x-alpha _{2})cdots (x-alpha _{n})}\u306e\u5f62\u306b\u56e0\u6570\u5206\u89e3\u3055\u308c\u3001\u03b11, \u03b12, …, \u03b1n \u306e\u4e2d\u306b 2 \u3064\u4ee5\u4e0a\u540c\u3058\u5024\u304c\u3042\u308b\u5834\u5408\u3001\u305d\u306e\u5024\u3092 f(x) \u306e\u91cd\u6839\u3068\u3044\u3046\u3002  \u65b9\u7a0b\u5f0f f(x) = 0 \u306e\u89e3\u306f\u4e00\u822c\u306b{y=f(x)y=0{displaystyle left{{begin{matrix}y&=&f(x)\\y&=&0end{matrix}}right.}\u3064\u307e\u308a xy-\u5ea7\u6a19\u7cfb\u306b\u304a\u3044\u3066 y = f(x) \u3068 x \u8ef8\u3068\u306e\u4ea4\u70b9\u306e x \u5ea7\u6a19\u3067\u3042\u308b\u3002 f(x)\u304c1\u5909\u6570\u591a\u9805\u5f0f\u306e\u3068\u304d\u3001 y = f(x) \u304cx=\u03b1\u3067 x \u8ef8\u306b\u63a5\u3059\u308b\u306a\u3089\u3001\u03b1\u306f f(x) \u306e\u91cd\u6839\u3068\u306a\u308b\u3002\u3057\u305f\u304c\u3063\u3066f(x)\u306fx=\u03b1\u3067\u306e\u5fae\u5206\u30820\u3068\u306a\u308a\u3001x=\u03b1\u304cf(x) \u306e\u91cd\u6839\u3067\u3042\u308b\u3053\u3068\u3068  {f(\u03b1)=0f\u2032(\u03b1)=0{displaystyle left{{begin{matrix}f(alpha )&=&0\\f'(alpha )&=&0end{matrix}}right.}\u3067\u3042\u308b\u3053\u3068\u306f\u540c\u5024\u3067\u3042\u308b\u3002\u4f53 K \u4e0a\u306e\u591a\u9805\u5f0f f(x) \u3068 K \u306e\u5143 \u03b1 \u306b\u5bfe\u3057\u3001(x – \u03b1)2 | f(x) \u304c\u6210\u7acb\u3059\u308b\u3068\u304d\u3001\u3059\u306a\u308f\u3061 2 \u4ee5\u4e0a\u306e\u81ea\u7136\u6570 k \u3068\u591a\u9805\u5f0f g(x) \u3067f(x)=(x\u2212\u03b1)kg(x){displaystyle f(x)=(x-alpha )^{k}g(x)}\u3092\u6e80\u305f\u3059\u3082\u306e\u304c\u5b58\u5728\u3059\u308b\u3068\u304d\u3001\u03b1 \u3092 f(x) \u306e\u91cd\u6839\u3068\u3044\u3046\u3002\u7279\u306b g(x) \u304c \u03b1 \u3092\u6839\u306b\u6301\u305f\u306a\u3044\u306a\u3089\u3070\u3001k \u3092\u6839 \u03b1 \u306e\u91cd\u8907\u5ea6\uff08\u3061\u3087\u3046\u3075\u304f\u3069\u3001multiplicity\uff09\u3068\u3044\u3046\u3002\u591a\u9805\u5f0f f(x) \u306e\u6839\u3092 \u03b11, \u03b12, …, \u03b1n \u3068\u3057\u3001\u305d\u306e\u5168\u4f53\u304b\u3089\u4f5c\u3089\u308c\u308b\u6700\u7c21\u4ea4\u4ee3\u5f0f\uff08\u5dee\u7a4d\uff09\u306e\u5e73\u65b9Df:=\u220f1\u2264ii\u2212\u03b1j)2{displaystyle D_{f}:=prod _{1leq i=\u2212ba,{displaystyle alpha +beta =-{frac {b}{a}},}\u03b1\u03b2=ca{displaystyle alpha beta ={frac {c}{a}}}\u304c\u6210\u308a\u7acb\u3061\u3001\u5224\u5225\u5f0f\u3059\u306a\u308f\u3061\u5dee\u7a4d\u306e\u4e8c\u4e57\u306f(\u03b1\u2212\u03b2)2=(\u03b1+\u03b2)2\u22124\u03b1\u03b2=(\u2212ba)2\u22124\u00d7ca=b2\u22124aca2{displaystyle (alpha -beta )^{2}=(alpha +beta )^{2}-4alpha beta =left(-{frac {b}{a}}right)^{2}-4times {frac {c}{a}}={frac {b^{2}-4ac}{a^{2}}}}\u3068\u306a\u308b\u3002a2 > 0 \u3067\u3042\u308b\u306e\u3067\u3001\u5b9f\u7528\u4e0a\u306f\u5206\u6bcd\u3092\u6383\u3063\u305f b2 – 4ac \u3092\u5224\u5225\u5f0f\u3068\u3057\u3066\u7528\u3044\u308b\u3053\u3068\u304c\u591a\u3044\u3002\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki14\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki14\/2022\/03\/17\/%e9%87%8d%e6%a0%b9-%e5%a4%9a%e9%a0%85%e5%bc%8f-wikipedia\/#breadcrumbitem","name":"\u91cd\u6839 (\u591a\u9805\u5f0f) – Wikipedia"}}]}]