Matematika

Pertanyaan

diberikan f(x) =2x^3-mx^2+13x+ n habis dibagi oleg (x^2+3x+). nilai dari 2m + n =
a. -18
b.-12
c.-6
d.6
e.18

mohon bantuannya ya pakai cara teriakasih

1 Jawaban

  • f(x)= 2x³ - mx² + 13x + n
    habis dibagi (x² + 3x + 2) --> sisa = 0
    x² + 3x +2 = 0
    (x +1)(x +2)= 0
    x = -1 atau x = - 2
    .
    f(-1) = 0 --> 2(-1)³- m(-1)² + 13(-1) + n = 0
    -2 - m - 13 + n = 0
    -m + n = 15
    m - n = - 15.....(1)
    .
    f(-2) =0 --> 2(-8) - m(4) + 13(-2) + n = 0
    -16 - 4m -26 +n = 0
    -4m +n = 42 ...(2)
    .
    (1), (2) eliminasi
    m - n = -15
    -4m + n = 24
    ....(+)...
    -3m = 9
    m = -3
    .
    m - n = 15
    n = m -15 = -3-15
    n = -18
    .
    2m + n = 2(-3) + (-18)
    2m + n = -6 -18 = - 24

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