{"id":136032,"date":"2017-07-31T11:46:30","date_gmt":"2017-07-31T04:46:30","guid":{"rendered":"https:\/\/video.quipper.com\/id\/blog\/?p=136032"},"modified":"2021-11-02T22:59:06","modified_gmt":"2021-11-02T15:59:06","slug":"ujian-nasional-2018-pelajari-soal-persamaan-pertidaksamaan-kuadrat","status":"publish","type":"post","link":"https:\/\/quipperhome.wpcomstaging.com\/matematika-un-sma\/ujian-nasional-2018-pelajari-soal-persamaan-pertidaksamaan-kuadrat\/","title":{"rendered":"Ujian Nasional 2018? Pelajari Soal Persamaan & Pertidaksamaan Kuadrat!"},"content":{"rendered":"

\"Ujian<\/a><\/p>\n

Hey<\/span><\/i> Quipperian. Gimana udah semakin mahir mengerjakan soal Matematika? Tentu, kan sering pantau artikel Quipper tentang soal dan pembahasan Matematika tema Logaritma, dan lainnya.<\/span><\/p>\n

Mau Kuliah Jurusan Matematika? Simak Sejenak Sejarah Logaritma John Napier!<\/a><\/h3>\n

Guys<\/span><\/i>, kalian sedari dini sangat boleh belajar dan berlatih mengerjakan soal Matematika untuk bekal UN 2018. Enggak ada ruginya kok. Malah kalian akan serasa mendapat hadiah ketika berjumpa soal Matematika saat UN berlangsung.<\/span><\/p>\n

Kali ini, bahasannya enggak kalah <\/span>kece<\/span><\/i>, persamaan dan pertidaksamaan kuadrat. <\/span><\/p>\n

Persamaan kuadrat merupakan persamaan dengan bentuk umum <\/span>y = ax<\/span><\/i>2<\/span><\/i> + bx + c = 0, <\/span><\/i>dengan<\/span> a\u22600. <\/span><\/i>Huruf <\/span>a, b, c, <\/span><\/i>disebut sebagai koefisien. Jadi, koefisien kuadrat <\/span>a<\/span><\/i> merupakan koefisien <\/span>x<\/span><\/i>2<\/span><\/i>, koefisien linier <\/span>b<\/span><\/i> adalah koefisien <\/span>x<\/span><\/i>, dan <\/span>c<\/span><\/i> merupakan koefisien konstan atau disebut juga suku bebas. <\/span><\/p>\n

Sementara pertidaksamaan kuadrat merupakan persamaan dengan bentuk umum;<\/span><\/p>\n

1) ax<\/span><\/i>2<\/span><\/i> + bx + c < 0; <\/span><\/i><\/p>\n

2) <\/span>ax<\/span><\/i>2<\/span><\/i> + bx + c \u2264 0;<\/span><\/i><\/p>\n

3) <\/span>ax<\/span><\/i>2<\/span><\/i> + bx + c \u2265 0;<\/span><\/i><\/p>\n

4) <\/span>ax<\/span><\/i>2<\/span><\/i> + bx + c > 0;<\/span><\/i><\/p>\n

Nilai-nilai yang memenuhi pertidaksamaan kuadrat disebut penyelesaian pertidaksamaan kuadrat. Agar lebih mudah memahami, kalian akan berseluncur mengerjakan latihan soal dan pembahasan persamaan dan pertidakasamaan kuadrat berikut. \u00a0<\/span><\/p>\n


\nLatihan Persamaan Soal 1<\/b><\/span><\/h2>\n

Persamaan <\/span>2<\/span>x<\/span><\/i>2<\/span> + <\/span>qx<\/span><\/i> + (<\/span>q<\/span><\/i>-1) = 0 <\/span>memiliki akar-akar <\/span>x<\/span>1<\/span> dan <\/span>x<\/span>2<\/span>. Jika <\/span>x<\/span>1<\/span>2<\/span> + <\/span>x<\/span>2<\/span>2 <\/span>= 4, <\/span>nilai <\/span>q<\/span><\/i> = …..
\n<\/span>
\nA. -6 & 2
\n<\/span>B. -5 & 3
\n<\/span>C. -4 & 4
\n<\/span>D. -3 & 5
\n<\/span>E. -2 & 6<\/span><\/p>\n

Jawaban E<\/span><\/p>\n

Pembahasan: <\/span><\/p>\n

Persamaan <\/span>2<\/span>x<\/span><\/i>2<\/span> + <\/span>qx<\/span><\/i> + (<\/span>q<\/span><\/i>-1) = 0<\/span><\/p>\n

a<\/span><\/i> = 2<\/span><\/p>\n

b<\/span><\/i> = <\/span>q<\/span><\/i><\/p>\n

c<\/span><\/i> = <\/span>q<\/span><\/i> \u2013 1<\/span><\/p>\n

x<\/span>1<\/span> + <\/span>x<\/span>2<\/span> = <\/span>-q<\/span>2<\/span><\/p>\n

x<\/span>1<\/span> + <\/span>x<\/span>2<\/span> = <\/span>q-1<\/span>2<\/span><\/p>\n

x<\/span>1<\/span>2<\/span> + <\/span>x<\/span>2<\/span>2 <\/span>= (<\/span>x<\/span>1<\/span> + <\/span>x<\/span>2<\/span>)<\/span>2<\/span> \u2013 2 <\/span>x<\/span>1<\/span> x<\/span>2<\/span><\/p>\n

(<\/span>-q<\/span>2<\/span>)<\/span>2<\/span> -2 (<\/span>q-1<\/span>2<\/span>) = 4 <\/span><\/p>\n

(<\/span>q<\/span>2<\/span>2<\/span>) -2 (<\/span>q-1<\/span>2<\/span>) = 4<\/span><\/p>\n

q<\/span>2<\/span>2<\/span> \u2013 <\/span>q<\/span><\/i> + 1 \u2013 4 = 0<\/span><\/p>\n

q<\/span>2<\/span>2<\/span> \u2013 <\/span>q<\/span><\/i> \u2013 3 = 0<\/span><\/p>\n

(<\/span>q<\/span><\/i> \u2013 6 ) (<\/span>q<\/span><\/i> + 2) = 0<\/span><\/p>\n

q<\/span><\/i> \u00a0– 6 = 0 atau <\/span>q<\/span>1<\/span>= 6<\/span><\/p>\n

q <\/span><\/i>\u2013 2 = 0 atau <\/span>q<\/span>2<\/span> = -2<\/span><\/p>\n

Latihan Persamaan Soal 2<\/b><\/h2>\n

Persamaan <\/span>ax<\/span><\/i>2<\/span> \u2013 5<\/span>x<\/span><\/i> + (<\/span>a<\/span><\/i> + 1) = 0, <\/span>mempunyai akar <\/span>p <\/span><\/i>dan<\/span> q<\/span><\/i>. Jika <\/span>p <\/span><\/i>+ <\/span>q <\/span><\/i>= 2<\/span>1<\/span>2<\/span> \u00a0maka nilai <\/span>a<\/span><\/i> sama dengan….
\n<\/span>
\nA. -1
\n<\/span>B. – <\/span>2<\/span>3
\n<\/span>C. 2<\/span>7
\n<\/span>D. 1
\n<\/span>E. 2<\/span><\/p>\n

Jawaban E<\/span><\/p>\n

Pembahasan:<\/span><\/p>\n

Dari persamaan <\/span>ax<\/span><\/i>2<\/span> \u2013 5<\/span>x<\/span><\/i> + (<\/span>a<\/span><\/i> + 1) = 0<\/span> diperoleh <\/span>a = a; b =-5; c = (a + 1); <\/span><\/i>x<\/span>1<\/span>= p; <\/span><\/i>x<\/span>2<\/span>=q<\/span><\/i><\/p>\n

x<\/span>1<\/span> + <\/span>x<\/span>2<\/span> = <\/span>p + q = <\/span><\/i>-a<\/span>b<\/span> = 2<\/span><\/i>1<\/span>2<\/span> \u00a0<\/span><\/i><\/p>\n

– <\/span><\/i>(-5)<\/span>a<\/span>= <\/span><\/i>2<\/span>1<\/span>2<\/span><\/p>\n

2<\/span>1<\/span>2<\/span> a = 5<\/span><\/i><\/p>\n

a = 2<\/span><\/i><\/p>\n

Latihan Persamaan Soal 3<\/b><\/h2>\n

Jika nilai diskriminan persamaan kuadrat<\/span> 2x<\/span><\/i>2<\/span><\/i>– 9x + c = 0 \u00a0<\/span><\/i>adalah<\/span> 121 <\/span><\/i>maka nilai<\/span> c = ….
\n<\/span><\/i>A. -8
\n<\/span>B. -5
\n<\/span>C. 2
\n<\/span>D. 5
\n<\/span>E. 8<\/span><\/p>\n

Jawaban B<\/span><\/p>\n

Pembahasan:<\/span><\/p>\n

Dari persamaan <\/span>2x<\/span><\/i>2<\/span><\/i>– 9x + c = 0 \u00a0<\/span><\/i>diperoleh <\/span>a = 2; b = -9; c = c <\/span><\/i><\/p>\n

Nilai diskriminan ditentukan dengan menggunakan rumus <\/span>d = b<\/span><\/i>2<\/span><\/i>– 4ac<\/span><\/i><\/p>\n

121 = (-9)<\/span><\/i>2<\/span><\/i>– 4 (2)(c)<\/span><\/i><\/p>\n

121 = 81 \u2013 8c<\/span><\/i><\/p>\n

8c = -40 <\/span><\/i><\/p>\n

c \u00a0= -5<\/span><\/i><\/p>\n

Latihan Persamaan Soal 4<\/b><\/h2>\n

Persamaan kuadrat yang akar-akarnya <\/span>5 <\/span><\/i>dan<\/span> -2 <\/span><\/i>adalah …
\n<\/span>A. x<\/span><\/i>2<\/span><\/i>+ 7x + 10 = 0
\n<\/span><\/i>B. x<\/span><\/i>2<\/span><\/i>– 7x + 10 = 0
\n<\/span><\/i>C. x<\/span><\/i>2<\/span><\/i>+ 3x + 10 = 0
\n<\/span><\/i>D. x<\/span><\/i>2<\/span><\/i>– 3x + 10 = 0
\n<\/span><\/i>E. x<\/span><\/i>2<\/span><\/i>– 3x – 10 = 0 \u00a0<\/span><\/i><\/p>\n

Jawaban E<\/span><\/p>\n

Pembahasan:<\/span><\/p>\n

Cara 1:<\/span><\/p>\n

(<\/span>x + <\/span><\/i>\u00a0<\/span>x<\/span>2<\/span>) (<\/span>x +<\/span><\/i> x<\/span>2<\/span>)= <\/span>0<\/span><\/i> diperoleh;<\/span><\/p>\n

x<\/span>1<\/span> = <\/span>5 <\/span><\/i>\u00a0dan <\/span>x<\/span>2<\/span>= <\/span>2<\/span><\/i> \u00a0<\/span><\/p>\n

(<\/span>x – 5<\/span><\/i>) (<\/span>x +<\/span><\/i> 2<\/span>)= <\/span>0<\/span><\/i><\/p>\n

x<\/span><\/i>2<\/span><\/i> \u2013 3x \u2013 10 = 0<\/span><\/i><\/p>\n

Cara 2:<\/span><\/p>\n

x<\/span><\/i>2<\/span><\/i> \u2013 (<\/span><\/i> x<\/span>1<\/span>+<\/span><\/i> x<\/span>2<\/span>) <\/span>x + <\/span><\/i>\u00a0<\/span>x<\/span>1<\/span> x<\/span>2<\/span> = <\/span>0<\/span><\/i><\/p>\n

x<\/span><\/i>2 <\/span><\/i>\u2013 [(5 + (2))] x \u00a0+ (5) (-2) = 0<\/span><\/i><\/p>\n

x<\/span><\/i>2<\/span><\/i> \u2013 3x \u00a0– 10 = 0<\/span><\/i><\/p>\n

Matematika Dasar SBMPTN Tentang Persamaan Kuadrat dan Pertidaksamaan Kuadrat<\/a><\/h3>\n

Latihan Pertidaksamaan Soal 1<\/b><\/h2>\n

Himpunan penyelesaian pertidaksamaan kuadrat <\/span>x<\/span><\/i>2<\/span><\/i> \u2013 x \u00a0– 12 > 0, <\/span><\/i>\u2208<\/span>R = …..<\/span><\/i><\/p>\n

A. {x I x < -3 \u00a0atau x > 4, x \u00a0<\/span><\/i>\u2208<\/span>R}
\n<\/span><\/i>B. {x I -3 < x < 4, x \u00a0<\/span><\/i>\u2208<\/span>R}
\n<\/span><\/i>C. {x I x < -1 \u00a0atau x > 6, x \u00a0<\/span><\/i>\u2208<\/span>R}
\n<\/span><\/i>D. {x I -2 < x < 6, x \u00a0<\/span><\/i>\u2208<\/span>R}
\n<\/span><\/i>E. {x I -4 < x < 3, x \u00a0<\/span><\/i>\u2208<\/span>R}<\/span><\/i><\/p>\n

Jawaban A<\/span><\/p>\n

Pembahasan:<\/span><\/p>\n

x<\/span><\/i>2<\/span><\/i> \u2013 x \u00a0– 12 > 0, <\/span><\/i>\u2208<\/span>R =<\/span><\/i><\/p>\n

(x + 3) (x -4) > 0 =<\/span><\/i><\/p>\n

x = -3 atau x = 4<\/span><\/i><\/p>\n

+++ 3 \u00a0– – – \u00a0\u00a04 +++<\/span><\/p>\n

HP <\/span>{x I x < -3 \u00a0atau x > 4, x \u00a0<\/span><\/i>\u2208<\/span>R}<\/span><\/i><\/p>\n

Latihan Pertidaksamaan Soal 2<\/b><\/h2>\n

Himpunan penyelesaian <\/span>x<\/span><\/i>2<\/span><\/i> \u2013 x \u00a0– 6 > 0 <\/span><\/i>untuk <\/span>x \u00a0<\/span><\/i>\u2208<\/span>R =
\n<\/span><\/i>
\nA. {x I x < -2 \u00a0atau x > 3, x \u00a0<\/span><\/i>\u2208<\/span>R}
\n<\/span><\/i>B. {x I x < -3 \u00a0atau x > 2, x \u00a0<\/span><\/i>\u2208<\/span>R}
\n<\/span><\/i>C. {x I x < -1 \u00a0atau x > 6, x \u00a0<\/span><\/i>\u2208<\/span>R}
\n<\/span><\/i>D. {x I -2 < x < 3, x \u00a0<\/span><\/i>\u2208<\/span>R}
\n<\/span><\/i>E. {x I -1 < x < 6, x \u00a0<\/span><\/i>\u2208<\/span>R}<\/span><\/i><\/p>\n

Jawaban A<\/span><\/p>\n

Pembahasan:<\/span><\/p>\n

x<\/span><\/i>2<\/span><\/i> \u2013 x \u00a0– 6 > 0 <\/span><\/i><\/p>\n

(x + 2) (x -3) > 0<\/span><\/i><\/p>\n

x = -2 atau x = 3<\/span><\/i><\/p>\n

+++ -2 \u00a0– – – \u00a0\u00a03 +++<\/span><\/p>\n

{x I x < -2 \u00a0atau x > 3, x \u00a0<\/span><\/i>\u2208<\/span>R}<\/span><\/i><\/p>\n

Latihan Pertidaksamaan Soal 3<\/b><\/h2>\n

Himpunan penyelesaian <\/span>x<\/span><\/i>2<\/span><\/i> \u2013 x \u00a0– 6 < 0 = ……<\/span><\/i><\/p>\n

A. {x I x \u2264 -3 \u00a0atau x \u2265 2 }
\n<\/span><\/i>B. {x I x \u2264 -2 \u00a0atau x \u2265 3 }
\n<\/span><\/i>C. {x I -3 \u2264 x \u2265 2 }
\n<\/span><\/i>D. {x I -2 \u2264 x \u2265 3 }
\n<\/span><\/i>E. {x I 2 \u2264 x \u2265 3 }<\/span><\/i><\/p>\n

Jawaban D<\/span><\/p>\n

Pembahasan: <\/span><\/p>\n

x<\/span><\/i>2<\/span><\/i> \u2013 x \u00a0– 6 < 0<\/span><\/i><\/p>\n

(x + 3) (x -2)< 0<\/span><\/i><\/p>\n

x = -3 atau x = 2<\/span><\/i><\/p>\n

+++ -3 \u00a0– – – \u00a02 +++<\/span><\/p>\n

{x I -2 \u2264 x \u2265 3 }<\/span><\/i><\/p>\n

Quipperian udah tahu kan beda persamaan dan pertidaksamaan kuadrat. Contoh dia atas justru memberikan gambaran utuh bagaimana beda keduanya melalui contoh soal dan pembahasannya. Semoga kalian semakin menguasai persamaan dan pertidaksamaan kuadrat agar semakin mudah mengerjakan soal Matematika UN mendatang. <\/span>Adios!<\/span><\/i>
\nPenulis: Rahmat Ali<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

Hey Quipperian. Gimana udah semakin mahir mengerjakan soal Matematika? Tentu, kan sering pantau artikel Quipper tentang soal dan pembahasan Matematika tema Logaritma, dan lainnya.…<\/p>\n","protected":false},"author":156446345,"featured_media":136042,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_monsterinsights_skip_tracking":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_wpcom_ai_launchpad_first_post":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[677999210],"tags":[],"ppma_author":[679386822],"class_list":["post-136032","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematika-un-sma"],"acf":[],"yoast_head":"\nUjian Nasional 2018? Pelajari Soal Persamaan & Pertidaksamaan Kuadrat!<\/title>\n<meta name=\"description\" content=\"Quipperian, Ujian Nasional 2018 baiknya nggak cuma ditunggu, tapi dipersiapkan dengan baik! Lihat dulu materi persamaan & pertidaksamaan kuadrat ini ya\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.quipper.com\/id\/blog\/matematika-un-sma\/ujian-nasional-2018-pelajari-soal-persamaan-pertidaksamaan-kuadrat\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Ujian Nasional 2018? Pelajari Soal Persamaan & Pertidaksamaan Kuadrat!\" \/>\n<meta property=\"og:description\" content=\"Quipperian, Ujian Nasional 2018 baiknya nggak cuma ditunggu, tapi dipersiapkan dengan baik! 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