Tentukan nilai A, B dan C jika diketahui :

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11x^2 + 4x + 12 = A(x^2+4) + (Bx+C) (2x+1) adalah……​

Tentukan nilai A, B dan C jika diketahui :

Jawaban Terkonfirmasi

Jawab:

A = 3, B = 4, C = 0

Penjelasan dengan langkah-langkah:

A(x² + 4) + (Bx + C)(2x + 1)

Ax² + 4A + 2Bx² + Bx + 2Cx + C

x²(A + 2B) + x(2C + B) + (4A + C) = 11x² + 4x + 12

A + 2B = 11

2C + B = 4

4A + C = 12

4C + 2B = 8

4C – A = -3

16C – 4A = -12

17C = 0

C = 0

0 – A = -3

A = 3

3 + 2B = 11

2B = 8

B = 4

Jawab:

Penjelasan dengan langkah-langkah:

F(x) = 11x^2 + 4x + 12 = A(x^2+4) + (Bx+C) (2x+1)\x^2+4 = 0 to x = pm sqrt{-4} = pm 2i, 2x+1 = 0to x = -dfrac{1}{2}\\F(2i) = 11cdot (2i)^2 + 4cdot 2i + 12 = Acdot 0 + (C+2Bi)cdot (1+4i)\-44+12 + 8i = -32+8i= C -8B + 2(2C+B)i\2C+B = 4, C-8B = -32to C = 8(B - 4)\16(B-4)+B = 4\16(B-4) = -(B-4) to B = 4to C = 0\

F(x) = 11x^2 + 4x + 12 = A(x^2+4) + 4x (2x+1)\displaystyle Fleft(0) = 12 = 4A + 0to A = 3

boxed{boxed{A = 3, B = 4, C = 0}}