{"id":242,"date":"2023-11-14T11:27:50","date_gmt":"2023-11-14T11:27:50","guid":{"rendered":"https:\/\/rumusmatematika.id\/?p=242"},"modified":"2023-11-17T03:43:02","modified_gmt":"2023-11-17T03:43:02","slug":"rumus-persamaan-kuadrat","status":"publish","type":"post","link":"https:\/\/tuturpedia.com\/rumusmatematika\/rumus-persamaan-kuadrat\/","title":{"rendered":"Rumus Persamaan Kuadrat Dan 7 Contohnya"},"content":{"rendered":"

Rumus persamaan kuadrat<\/a> adalah salah satu konsep matematika yang mendalam dan bermanfaat dalam pemodelan berbagai fenomena dalam kehidupan sehari-hari.<\/h2>\n

Artikel ini akan membahas rumus persamaan kuadrat dan memberikan tujuh contoh yang dimulai dari yang mudah hingga yang paling sulit, memandu pembaca melalui kompleksitas konsep tersebut.<\/p>\n

\"%rumus<\/p>\n

Rumus Persamaan Kuadrat<\/strong><\/a><\/p>\n

Persamaan kuadrat umumnya ditulis dalam bentuk \ufffd\ufffd2+\ufffd\ufffd+\ufffd=0<\/span>a<\/span>x<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>b<\/span>x<\/span>+<\/span><\/span>c<\/span>=<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>, di mana \ufffd<\/span>a<\/span><\/span><\/span><\/span><\/span>, \ufffd<\/span>b<\/span><\/span><\/span><\/span><\/span>, dan \ufffd<\/span>c<\/span><\/span><\/span><\/span><\/span> adalah konstanta, dan \ufffd<\/span>x<\/span><\/span><\/span><\/span><\/span> adalah variabel. Solusi persamaan ini dapat ditemukan menggunakan rumus kuadratik: \ufffd=\u2212\ufffd\u00b1\ufffd2\u22124\ufffd\ufffd2\ufffd<\/span>x<\/span>=<\/span><\/span>2a<\/span><\/span><\/span>\u2212b<\/span>\u00b1<\/span>b<\/span>2<\/span><\/span><\/span>\u2212<\/span>4a<\/span>c<\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>.<\/p>\n

Contoh 1: Persamaan Kuadrat Sederhana<\/strong><\/p>\n

Misalkan kita punya persamaan \ufffd2\u22124=0<\/span>x<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>4<\/span>=<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>. Dalam hal ini, \ufffd=1<\/span>a<\/span>=<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>, \ufffd=0<\/span>b<\/span>=<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>, dan \ufffd=\u22124<\/span>c<\/span>=<\/span><\/span>\u2212<\/span>4<\/span><\/span><\/span><\/span><\/span>. Kita dapat menggunakan rumus kuadratik untuk menemukan solusinya.<\/p>\n

\ufffd=\u22120\u00b102\u22124(1)(\u22124)2(1)<\/span>x<\/span>=<\/span><\/span>2(<\/span>1)<\/span><\/span><\/span>\u22120\u00b1<\/span>02<\/span><\/span><\/span>\u2212<\/span>4(<\/span>1)<\/span>(<\/span>\u22124)<\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\ufffd=\u00b1162<\/span>x<\/span>=<\/span><\/span>2<\/span><\/span>\u00b116<\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\ufffd=\u00b142<\/span>x<\/span>=<\/span><\/span>2<\/span><\/span>\u00b14<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\ufffd=\u22122\u00a0atau\u00a0\ufffd=2<\/span>x<\/span>=<\/span><\/span>\u2212<\/span>2<\/span>\u00a0<\/span>atau<\/span><\/span>\u00a0<\/span>x<\/span>=<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/p>\n

Contoh 2: Persamaan Kuadrat dengan Diskriminan Nol<\/strong><\/p>\n

Mari kita lihat persamaan \ufffd2\u22124\ufffd+4=0<\/span>x<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>4<\/span>x<\/span>+<\/span><\/span>4<\/span>=<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>. Dalam hal ini, diskriminannya (\ufffd2\u22124\ufffd\ufffd<\/span>b<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>4<\/span>a<\/span>c<\/span><\/span><\/span><\/span><\/span>) adalah 0.<\/p>\n

\ufffd=\u2212(\u22124)\u00b1(\u22124)2\u22124(1)(4)2(1)<\/span>x<\/span>=<\/span><\/span>2(<\/span>1)<\/span><\/span><\/span>\u2212(<\/span>\u22124)<\/span>\u00b1<\/span>(<\/span>\u22124)2<\/span><\/span><\/span><\/span>\u2212<\/span>4(<\/span>1)<\/span>(<\/span>4)<\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\ufffd=4\u00b102<\/span>x<\/span>=<\/span><\/span>2<\/span><\/span>4\u00b1<\/span>0<\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\ufffd=42<\/span>x<\/span>=<\/span><\/span>2<\/span><\/span>4<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\ufffd=2<\/span>x<\/span>=<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/p>\n

Contoh 3: Persamaan Kuadrat dengan Diskriminan Negatif<\/strong><\/p>\n

Kita akan melihat persamaan \ufffd2+2\ufffd+5=0<\/span>x<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>2<\/span>x<\/span>+<\/span><\/span>5<\/span>=<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>. Dalam hal ini, diskriminannya negatif, yang berarti solusinya bersifat kompleks.<\/p>\n

\ufffd=\u22122\u00b122\u22124(1)(5)2(1)<\/span>x<\/span>=<\/span><\/span>2(<\/span>1)<\/span><\/span><\/span>\u22122\u00b1<\/span>22<\/span><\/span><\/span>\u2212<\/span>4(<\/span>1)<\/span>(<\/span>5)<\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\ufffd=\u22122\u00b1\u2212162<\/span>x<\/span>=<\/span><\/span>2<\/span><\/span>\u22122\u00b1<\/span>\u221216<\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\ufffd=\u22122\u00b14\ufffd2<\/span>x<\/span>=<\/span><\/span>2<\/span><\/span>\u22122\u00b1<\/span>4i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\ufffd=\u22121\u00b12\ufffd<\/span>x<\/span>=<\/span><\/span>\u2212<\/span>1<\/span>\u00b1<\/span><\/span>2<\/span>i<\/span><\/span><\/span><\/span><\/span><\/p>\n

Contoh 4: Persamaan Kuadrat dengan Koefisien \ufffd<\/span>a<\/span><\/span><\/span><\/span><\/span> Lebih Besar dari 1<\/strong><\/p>\n

Pertimbangkan persamaan 2\ufffd2\u22123\ufffd+1=0<\/span>2<\/span>x<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>3<\/span>x<\/span>+<\/span><\/span>1<\/span>=<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>. Kita dapat menggunakan rumus kuadratik untuk mencari solusinya.<\/p>\n

\ufffd=3\u00b1(\u22123)2\u22124(2)(1)2(2)<\/span>x<\/span>=<\/span><\/span>2(<\/span>2)<\/span><\/span><\/span>3\u00b1<\/span>(<\/span>\u22123)2<\/span><\/span><\/span><\/span>\u2212<\/span>4(<\/span>2)<\/span>(<\/span>1)<\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\ufffd=3\u00b114<\/span>x<\/span>=<\/span><\/span>4<\/span><\/span>3\u00b1<\/span>1<\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\ufffd=3\u00b114<\/span>x<\/span>=<\/span><\/span>4<\/span><\/span>3\u00b1<\/span>1<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\ufffd=1\u00a0atau\u00a0\ufffd=12<\/span>x<\/span>=<\/span><\/span>1<\/span>\u00a0<\/span>atau<\/span><\/span>\u00a0<\/span>x<\/span>=<\/span><\/span>2<\/span><\/span>1<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

Contoh 5: Persamaan Kuadrat Tak Linear<\/strong><\/p>\n

Mari kita eksplorasi persamaan tak linear seperti \ufffd4\u221216=0<\/span>x<\/span>4<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>16<\/span>=<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>. Meskipun bentuknya bukan \ufffd\ufffd2+\ufffd\ufffd+\ufffd<\/span>a<\/span>x<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>b<\/span>x<\/span>+<\/span><\/span>c<\/span><\/span><\/span><\/span><\/span>, kita dapat memanipulasi persamaan untuk membawanya ke dalam bentuk kuadrat.<\/p>\n

\ufffd4\u221216=(\ufffd2\u22124)(\ufffd2+4)=0<\/span>x<\/span>4<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>16<\/span>=<\/span><\/span>(<\/span>x<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>4<\/span>)<\/span>(<\/span>x<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>4<\/span>)<\/span>=<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/p>\n

Solusinya adalah \ufffd=\u00b12<\/span>x<\/span>=<\/span><\/span>\u00b1<\/span>2<\/span><\/span><\/span><\/span><\/span> dan \ufffd=\u00b12\ufffd<\/span>x<\/span>=<\/span><\/span>\u00b1<\/span>2<\/span>i<\/span><\/span><\/span><\/span><\/span>.<\/p>\n

Contoh 6: Persamaan Kuadrat dengan Koefisien Desimal<\/strong><\/p>\n

Misalkan kita punya persamaan 0.5\ufffd2\u22123\ufffd+4=0<\/span>0.5<\/span>x<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>3<\/span>x<\/span>+<\/span><\/span>4<\/span>=<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>. Proses penyelesaiannya sama seperti sebelumnya.<\/p>\n

\ufffd=3\u00b1(\u22123)2\u22124(0.5)(4)2(0.5)<\/span>x<\/span>=<\/span><\/span>2(<\/span>0.5)<\/span><\/span><\/span>3\u00b1<\/span>(<\/span>\u22123)2<\/span><\/span><\/span><\/span>\u2212<\/span>4(<\/span>0.5)<\/span>(<\/span>4)<\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\ufffd=3\u00b19\u221281<\/span>x<\/span>=<\/span><\/span>1<\/span><\/span>3\u00b1<\/span>9\u2212<\/span>8<\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\ufffd=3\u00b111<\/span>x<\/span>=<\/span><\/span>1<\/span><\/span>3\u00b1<\/span>1<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\ufffd=4\u00a0atau\u00a0\ufffd=2<\/span>x<\/span>=<\/span><\/span>4<\/span>\u00a0<\/span>atau<\/span><\/span>\u00a0<\/span>x<\/span>=<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/p>\n

Contoh 7: Persamaan Kuadrat dengan Dua Variabel<\/strong><\/p>\n

Terakhir, pertimbangkan persamaan kuadrat dengan dua variabel, misalnya 3\ufffd2+4\ufffd\ufffd+\ufffd2=0<\/span>3<\/span>x<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>4<\/span>x<\/span>y<\/span>+<\/span><\/span>y<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>. Penyelesaian persamaan ini melibatkan teknik faktorisasi dan pemahaman yang lebih mendalam tentang persamaan kuadrat dalam konteks multivariabel.<\/p>\n

Kesimpulan<\/strong><\/p>\n

Rumus persamaan kuadrat adalah alat matematika yang kuat dan serbaguna. Dari contoh-contoh sederhana hingga yang lebih kompleks, pemahaman terhadap konsep ini menjadi landasan bagi berbagai aplikasi di berbagai bidang ilmu. Melalui pembahasan ini, diharapkan pembaca dapat memahami rumus persamaan kuadrat dan mengaplikasikannya dalam pemecahan masalah matematika yang lebih canggih.<\/p>\n","protected":false},"excerpt":{"rendered":"

Rumus persamaan kuadrat adalah salah satu konsep matematika yang mendalam dan bermanfaat dalam pemodelan berbagai fenomena dalam kehidupan sehari-hari. Artikel […]<\/p>\n","protected":false},"author":1,"featured_media":244,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[207,214,215,213,210,53,201,204,211,212,216,197,206,198,199,200,202,203,208,205,209],"class_list":["post-242","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-rumus-matematika","tag-bentuk-persamaan-kuadrat","tag-contoh-soal-melengkapi-kuadrat-sempurna","tag-contoh-soal-melengkapkan-kuadrat-sempurna","tag-contoh-soal-persamaan-kuadrat-baru","tag-contoh-soal-rumus-abc","tag-keyword","tag-kuadrat-sempurna","tag-materi-persamaan-kuadrat","tag-menyusun-persamaan-kuadrat","tag-menyusun-persamaan-kuadrat-baru","tag-persamaan-akar-kuadrat","tag-persamaan-kuadrat","tag-persamaan-kuadrat-baru","tag-rumus-abc","tag-rumus-abc-persamaan-kuadrat","tag-rumus-abc-pertidaksamaan-kuadrat","tag-rumus-kuadrat","tag-rumus-kuadrat-sempurna","tag-rumus-melengkapkan-kuadrat-sempurna","tag-rumus-persamaan","tag-rumus-persamaan-kuadrat-baru"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/tuturpedia.com\/rumusmatematika\/wp-json\/wp\/v2\/posts\/242","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/tuturpedia.com\/rumusmatematika\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/tuturpedia.com\/rumusmatematika\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/tuturpedia.com\/rumusmatematika\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/tuturpedia.com\/rumusmatematika\/wp-json\/wp\/v2\/comments?post=242"}],"version-history":[{"count":5,"href":"https:\/\/tuturpedia.com\/rumusmatematika\/wp-json\/wp\/v2\/posts\/242\/revisions"}],"predecessor-version":[{"id":629,"href":"https:\/\/tuturpedia.com\/rumusmatematika\/wp-json\/wp\/v2\/posts\/242\/revisions\/629"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/tuturpedia.com\/rumusmatematika\/wp-json\/wp\/v2\/media\/244"}],"wp:attachment":[{"href":"https:\/\/tuturpedia.com\/rumusmatematika\/wp-json\/wp\/v2\/media?parent=242"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/tuturpedia.com\/rumusmatematika\/wp-json\/wp\/v2\/categories?post=242"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/tuturpedia.com\/rumusmatematika\/wp-json\/wp\/v2\/tags?post=242"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}