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Bukti Rumus Kuadrat abc

September 5, 2010 Tinggalkan komentar Go to comments

Semasa SMU kita mengenal bentuk rumus kuadrat abc, seperti \left (x _{1};x_{2} \right )=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\LARGE Persamaan ini digunakan untuk memperkirakan akar-akar penyelesaian persamaan kuadrat, kadang menjadi alat ampuh bila akar penyelesaian yang dihasilkan berupa akar irrasional. Tapi pernahkah kita berpikir darimana asal rumus legendaris tersebut? Bila Anda tidak tahu darimana asalnya jangan kecewa dulu, karena banyak anak SMU jaman sekarang yang tidak mengetahuinya juga. Tulisan berikut membuktikan darimana rumus tersebut berasal… Kita mulai dari fungsi kuadrat ax^{2}+bx+c=0\huge

Pindah koefisien c ke ruas kanan dan kemudian kedua ruas kita bagi dengan a\huge , didapat x^{2}+\frac{bx}{a}=-\frac{c}{a}\huge

Selanjutnya kita ubah sisi kiri dengan melengkapakan kuadrat sempurna menjadi

\left ( x+\frac{b}{2a} \right )^{2}-\frac{b^{2}}{4a^{2}}=-\frac{c}{a}\huge

Selanjutnya bentuk \frac{b^{2}}{4a^{2}}\huge

kita pindahkan keruas kanan sehingga menjadi \left ( x+\frac{b}{2a} \right )^{2}=\frac{b^{2}-4ac}{4a^{2}}\huge

Dari sini akarkan kedua ruas menjadi x+\frac{b}{2a}=\sqrt{\frac{b^{2}-4ac}{4a^{2}}}\huge

Kita rapihkan, didapatkan rumus legendaris tersebut x=-\frac{b}{2a}\pm \sqrt{\frac{b^{2}-4ac}{4a^{2}}}\huge

atau bila disederhanakan menjadi \left (x _{1};x_{2} \right )=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\LARGE

Bagaimana? 🙂

Kategori:Asah Otak, Ada yang Bisa? Tag:, , ,
  1. juanda hasugian
    November 15, 2010 pukul 3:16 pm
    Balas

    keren tp sebelum baca gua jg dah tau bro.

  2. juanda hasugian
    November 15, 2010 pukul 3:20 pm
    Balas

    rumus abc nya masih salah dalam rumus anda membuat b padahal seharusnya itu -b

  3. juanda hasugian
    November 15, 2010 pukul 3:34 pm
    Balas

    penulisan persamaan kuadratnya masPersamaan kuadrat anda masih salah anda membuat persamaanya y=a” +bx =c padahal seharusnya y=ax”+bx+c.ih salah anda membuat y=a2+bx+c

  4. twinhammer
    November 19, 2010 pukul 11:25 am
    Balas

    wkwkw, maklum mas penulisan latexnya.
    sudah saya perbaiki.
    tks atas responnya

  5. iva
    Maret 8, 2012 pukul 1:50 pm
    Balas

    kalau pembuktian rumus menyusun fungsi kuadrat bagaiman caranya?

  6. twinhammer
    Maret 8, 2012 pukul 2:44 pm
    Balas

    waw luar biasa hidup lagi komennya setalah ditinggal 2 tahun. Untuk mas Iva, Klo menyusun fungsi juadrat,saya pake persamaan:

    x² – (jumlah akar-akar pers. kuadrat baru)x + ((hasil kali akar-akar pers. kuadrat baru).

    Selesai…

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