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

Interval nilai p yang menyebabkan fungsi kuadrat f left parenthesis x right parenthesis equals left parenthesis p minus 2 right parenthesis x squared plus 2 p x plus p plus 3 definit positif adalah....

  1. p < 2

  2. p < 6

  3. p > 2

  4. p > 6

  5. 2 < p < 6

Jawaban:

Syarat space dari space suatu space fungsi space straight f left parenthesis straight x right parenthesis equals ax squared plus bx plus straight c space definit space positif space adalah space colon  straight D less than 0 space dan space straight a greater than 0    Sehingga space supaya space fungsi space straight f left parenthesis straight x right parenthesis equals left parenthesis straight p minus 2 right parenthesis straight x squared plus 2px plus straight p plus 3 space definit space positif comma space maka  bold D bold less than bold 0  open parentheses 2 straight p close parentheses squared minus 4 open parentheses straight p minus 2 close parentheses open parentheses straight p plus 3 close parentheses less than 0  4 straight p squared minus 4 open parentheses straight p squared plus straight p minus 6 close parentheses less than 0  4 straight p squared minus 4 straight p squared minus 4 straight p plus 24 less than 0  minus 4 straight p less than negative 24  straight p greater than 6... left parenthesis 1 right parenthesis    bold a bold greater than bold 0 space  straight p minus 2 greater than 0 rightwards double arrow straight p greater than 2... left parenthesis 2 right parenthesis    Dari space irisan space syarat space left parenthesis 1 right parenthesis space dan space left parenthesis 2 right parenthesis comma space maka space didapat space  straight p greater than 6

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