Roboguru

Akar-akar persamaan adalah dan . Jika dan a > 0 ma...

Akar-akar persamaan x squared plus left parenthesis a minus 1 right parenthesis x plus 2 equals 0 adalah alpha dan beta. Jika alpha equals 2 beta dan a > 0 maka nilai a=.....

  1. 2

  2. 3

  3. 4

  4. 6

  5. 8

Jawaban:

Jika space persamaan space kuadrat space ax squared plus bx plus straight c equals 0 space memiliki space akar minus akar space straight alpha space dan space straight beta comma space maka straight alpha plus straight beta equals negative straight b over straight a αβ equals straight c over straight a Persamaan space kuadrat space straight x squared plus open parentheses straight a minus 1 close parentheses straight x plus 2 equals 0 space memiliki space akar – akar space straight alpha space dan space straight beta comma space di space mana space straight alpha equals 2 straight beta comma space berarti space αβ equals 2 over 1 left parenthesis 2 straight beta right parenthesis straight beta equals 2 2 straight beta squared equals 2 straight beta squared equals 1 straight beta equals 1 space atau space straight beta equals negative 1 Maka Untuk space straight beta equals 1 rightwards arrow straight alpha equals 2 open parentheses 1 close parentheses equals 2 Sehingga space straight alpha plus straight beta equals negative fraction numerator straight a minus 1 over denominator 1 end fraction 2 plus 1 equals negative straight a plus 1 straight a equals negative 2 Untuk space straight beta equals negative 1 rightwards arrow straight alpha equals 2 open parentheses negative 1 close parentheses equals negative 2 Sehingga space straight alpha plus straight beta equals negative fraction numerator straight a minus 1 over denominator 1 end fraction minus 2 minus 1 equals negative straight a plus 1 straight a equals 4 Karena space straight a greater than 0 comma space maka space straight a equals 4

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