数学 当f(x)除以4-x和2x+3时,余数分别是13和2。求f(x)除以2x눀-5x-12的余式

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2025-03-13 11:54:24
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回答1:

2x^2-5x-12 = (x-4)(2x+3)
f(x) = p(x) (4-x) + 13
f(x) =q(x) (2x+3) + 2
f(x) = r(x)(2x^2-5x-12) + ax+b
f(4) =13
4a+b=13 (1)
f(-3/2) = 2
(-3/2)a +b = 2 (2)
(1)-(2)
(11/2)a = 11
a=2
from (1)
4a+b=13
8+b=13
b=5
(a,b) = (2,5)
f(x)除以2x²-5x-12的余式 : 2x +5