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Interval nilai p yang menyebabkan fungsi kuadrat f ( x ) = ( p − 2 ) x 2 + 2 p x + p + 3 definit positif adalah....

Interval nilai p yang menyebabkan fungsi kuadrat definit positif adalah....

  1. p < 2

  2. p < 6

  3. p > 2

  4. p > 6

  5. 2 < p < 6

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Y. Endah

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

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Pembahasan

F u n g s i space K u a d r a t space f left parenthesis x right parenthesis space equals space left parenthesis p minus 2 right parenthesis x ² space plus space 2 p x space plus space p plus 3 space  S y a r a t space d e f i n i t space p o s i t i f space  left parenthesis 1 right parenthesis space a space greater than space 0 space left parenthesis 2 right parenthesis  space D space less than space 0 space space    left parenthesis 1 right parenthesis  space space space space space space a space greater than space 0 space  p space minus space 2 space greater than space 0  space space space space space space p space greater than space 2    space left parenthesis 2 right parenthesis  space space space space space space space space space space space space space space space space space space space space space space space space space space D space less than space 0 space  left parenthesis 2 p right parenthesis ² space minus space 4 space left parenthesis p minus 2 right parenthesis left parenthesis p plus 3 right parenthesis space less than space 0 space  4 p ² space minus space 4 space left parenthesis p ² space plus space p space minus space 6 right parenthesis space less than space 0 space  4 p ² space minus space 4 p ² space minus space 4 p space plus space 24 space less than space 0  space space space space space space space space space space space space space space minus space 4 p space plus space 24 space less than space 0  space space space space space space space space space space space space space space space space space space space space space minus space 4 p space less than space minus space 24  space space space space space space space space space space space space space space space space space space space space space space space space space p space greater than space 6 space  D a r i space left parenthesis 1 right parenthesis space d a n space left parenthesis 2 right parenthesis space d i p e r o l e h space h a s i l space p space greater than space 6

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Diketahui fungsi kuadrat dinyatakan dengan f ( x ) = x 2 + p x − 2 p − 3 . Jika fungsi tersebut tidak memotong sumbu X, nilai p yang memenuhi adalah ....

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