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[ UN 2012 ] Akar − akar persamaan kuadrat x 2 + ax − 4 = 0 adalah p dan q . Jika p 2 − 2 pq + q 2 = 8 a . Maka nilai a = ⋯

  1. -8

  2. -4

  3. 4

  4. 6

  5. 8

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begin mathsize 14px style straight p squared minus 2 pq plus straight q squared equals 8 straight a space left parenthesis straight p minus straight q right parenthesis squared equals 8 straight a horizontal ellipsis left parenthesis straight i right parenthesis space  Dari space persamaan space kuadrat space dapat space diperoleh colon space straight p minus straight q equals fraction numerator square root of straight D over denominator straight a end fraction equals fraction numerator square root of left parenthesis straight a squared minus 4 left parenthesis 1 right parenthesis left parenthesis negative 4 right parenthesis space right parenthesis end root over denominator 1 end fraction straight p minus straight q space equals square root of left parenthesis straight a squared minus 4 left parenthesis 1 right parenthesis left parenthesis negative 4 right parenthesis space right parenthesis end root equals square root of left parenthesis straight a squared plus 16 right parenthesis end root  Maka space substitusi space nilai space straight p minus straight q space ke space Persamaan space left parenthesis straight i right parenthesis space open parentheses square root of left parenthesis straight a squared plus 16 right parenthesis end root close parentheses squared equals 8 straight a space straight a squared plus 16 equals 8 straight a space straight a squared minus 8 straight a plus 16 equals 0 space left parenthesis straight a minus 4 right parenthesis squared equals 0 space straight a equals 4 space Jadi comma space nilai space straight a space adalah space 4. end style

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