Matematika

Pertanyaan

tolong nomer 10
pakek cara ya.. makasih
tolong nomer 10 pakek cara ya.. makasih

1 Jawaban

  • g(x) = x⁴+ 2x³-ax²-14x+b
    x²+3x-4 => (x+4)(x-1), x=-4 V x=1

    g(-4) => (-4)⁴ + 2(-4)³ - a(-4)² - 14(-4) + b = 0
    => 256 - 128 -16a + 56 + b = 0
    => -16a + b = -184 (i)

    g(1) => (1)⁴ + 2(1)³ - a(1)² - 14(1) + b = 0
    => 1 + 2 - a - 14 + b = 0
    => -a + b = 11 (ii)

    eliminasi (i) dan (ii)
    -16a+b=-184
    -a+b=11
    _______________-
    -15a = -195
    a = 39

    subs nilai a ke (ii)
    -(39) + b = 11
    b = 50

    masukkan nilai a dan b ke g(x)
    g(x)= x⁴+2x³-39x²-14x+50

    soalnya jika g(x) dibagi x+1 maka bersisa...
    x+1 = 0
    x = -1

    *skema horner

    | 1 2. -39. -14. 50
    x=-1 | -1. -1. 40. -26
    ___________________________ +
    1 1. -40. 26. 24

    jadi sisanya ialah 24 (E)