Kegiatan Menemukan Rumus Penyelesaian Persamaan Kuadrat Lengkapilah isian pada pengerjaan berikut! ⇔​ax2+bx+cax2+bx​==​0−c​ Kedua ruas dikalikan dengan a1​ agar koefisien x2 menjadi 1. ⇔⇔​a1​(ax2+bx)x2+ab​x​==​a1​(...)−......​​ Kedua ruas ditambah dengan kuadrat dari (21​×ab​). Bentuk terakhir disebut rumus penyelesaian persamaan kuadrat, atau lebih dikenal dengan istilah rumus abc.

Pertanyaan

Kegiatan

Menemukan Rumus Penyelesaian Persamaan Kuadrat

Lengkapilah isian pada pengerjaan berikut!

table attributes columnalign center right center left end attributes row blank cell a x squared plus b x plus c end cell equals 0 row left right double arrow cell a x squared plus b x end cell equals cell negative c end cell end table

Kedua ruas dikalikan dengan 1 over a agar koefisien x squared menjadi 1.

table attributes columnalign center right center left end attributes row left right double arrow cell 1 over a open parentheses a x squared plus b x close parentheses end cell equals cell 1 over a open parentheses... close parentheses end cell row left right double arrow cell x squared plus b over a x end cell equals cell negative fraction numerator... over denominator... end fraction end cell end table

Kedua ruas ditambah dengan kuadrat dari open parentheses 1 half cross times b over a close parentheses.

table attributes columnalign center right center left end attributes row left right double arrow cell x squared plus b over a x plus open parentheses fraction numerator b over denominator 2 a end fraction close parentheses squared end cell equals cell negative fraction numerator... over denominator... end fraction plus open parentheses fraction numerator... over denominator... end fraction close parentheses squared end cell row left right double arrow cell open parentheses x plus fraction numerator... over denominator... end fraction close parentheses squared end cell equals cell negative fraction numerator... over denominator... end fraction plus fraction numerator... over denominator... end fraction end cell row left right double arrow cell open parentheses x plus fraction numerator... over denominator... end fraction close parentheses squared end cell equals cell negative fraction numerator... over denominator... end fraction plus fraction numerator... over denominator... end fraction space leftwards arrow p e n y e b u t end cell row blank blank blank cell space space space space space space space space space space space space space space space space space space space space space space d i s a m a k a n end cell row left right double arrow cell open parentheses x plus fraction numerator... over denominator... end fraction close parentheses squared end cell equals cell fraction numerator... space minus space.... over denominator... end fraction end cell row left right double arrow cell x plus fraction numerator... over denominator... end fraction end cell equals cell plus-or-minus square root of open parentheses fraction numerator... space minus space... over denominator... end fraction close parentheses end root end cell row left right double arrow cell x plus fraction numerator... over denominator... end fraction end cell equals cell plus-or-minus fraction numerator square root of... space minus space... end root over denominator square root of... end root end fraction end cell row left right double arrow cell x plus fraction numerator... over denominator... end fraction end cell equals cell plus-or-minus fraction numerator square root of... space minus space... end root over denominator... end fraction end cell row left right double arrow x equals cell negative fraction numerator... over denominator... end fraction plus-or-minus fraction numerator square root of open parentheses... space minus space... close parentheses end root over denominator... end fraction end cell row left right double arrow x equals cell fraction numerator negative... plus-or-minus square root of... space minus space... end root over denominator... end fraction end cell end table

Bentuk terakhir disebut rumus penyelesaian persamaan kuadrat, atau lebih dikenal dengan istilah rumus abc.

N. Puspita

Master Teacher

Jawaban terverifikasi

Pembahasan

Kegiatan

Menemukan Rumus Penyelesaian Persamaan Kuadrat

Lengkapilah isian pada pengerjaan berikut!

table attributes columnalign center right center left end attributes row blank cell a x squared plus b x plus c end cell equals 0 row left right double arrow cell a x squared plus b x end cell equals cell negative c end cell end table

Kedua ruas dikalikan dengan 1 over a agar koefisien x squared menjadi 1.

table attributes columnalign center right center left end attributes row left right double arrow cell 1 over a open parentheses a x squared plus b x close parentheses end cell equals cell 1 over a open parentheses negative c close parentheses end cell row left right double arrow cell x squared plus b over a x end cell equals cell negative c over a end cell end table

Kedua ruas ditambah dengan kuadrat dari open parentheses 1 half cross times b over a close parentheses.

table attributes columnalign center right center left end attributes row left right double arrow cell x squared plus b over a x plus open parentheses fraction numerator b over denominator 2 a end fraction close parentheses squared end cell equals cell negative c over a plus open parentheses fraction numerator b over denominator 2 a end fraction close parentheses squared end cell row left right double arrow cell open parentheses x plus fraction numerator b over denominator 2 a end fraction close parentheses squared end cell equals cell negative c over a plus fraction numerator b squared over denominator 4 a squared end fraction end cell row left right double arrow cell open parentheses x plus fraction numerator b over denominator 2 a end fraction close parentheses squared end cell equals cell negative fraction numerator 4 a c over denominator 4 a squared end fraction plus fraction numerator b squared over denominator 4 a squared end fraction space leftwards arrow p e n y e b u t end cell row blank blank blank cell space space space space space space space space space space space space space space space space space space space space space space d i s a m a k a n end cell row left right double arrow cell open parentheses x plus fraction numerator b over denominator 2 a end fraction close parentheses squared end cell equals cell fraction numerator b squared space minus space 4 a c over denominator 4 a squared end fraction end cell row left right double arrow cell x plus fraction numerator b over denominator 2 a end fraction end cell equals cell plus-or-minus square root of open parentheses fraction numerator b squared space minus space 4 a c over denominator 4 a squared end fraction close parentheses end root end cell row left right double arrow cell x plus fraction numerator b over denominator 2 a end fraction end cell equals cell plus-or-minus fraction numerator square root of b squared space minus space 4 a c end root over denominator square root of 4 a squared end root end fraction end cell row left right double arrow cell x plus fraction numerator b over denominator 2 a end fraction end cell equals cell plus-or-minus fraction numerator square root of b squared space minus space 4 a c end root over denominator 2 a end fraction end cell row left right double arrow x equals cell negative fraction numerator b over denominator 2 a end fraction plus-or-minus fraction numerator square root of b squared space minus space 4 a c end root over denominator 2 a end fraction end cell row left right double arrow x equals cell fraction numerator negative b plus-or-minus square root of b squared space minus space 4 a c end root over denominator 2 a end fraction end cell end table

Bentuk terakhir disebut rumus penyelesaian persamaan kuadrat, atau lebih dikenal dengan istilah rumus abc.

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