Question

Diketahui f(x)=2x^3-mx^2+13x+n habis dibagi oleh (x^2+3x+2).Nilai dari 2m+n = ....

Answer 1

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Dalil Sisa
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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
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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)
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f(-2) =0 --> 2(-8) - m(4) + 13(-2) + n = 0
-16 - 4m -26 +n = 0
-4m +n = 42 ...(2)
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(1), (2) eliminasi
m - n = -15
-4m + n = 24
....(+)...
-3m  = 9
m = -3
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m - n = 15
n  = m -15 = -3-15
n = -18
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2m + n = 2(-3) + (-18)
2m + n = -6 -18 = - 24