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ce maths 2002 mc 38
發問:
The remainder when x^2 + ax + b is divided by x+2 is -4. The remainder when ax^2 + bx +1 is divided by x-2 is 9. The value of a is
最佳解答:
The remainder when x^2 + ax + b is divided by x+2 is -4. It means that (-2)^2 - 2a +b = -4 or 2a - b = 8 --------(1) The remainder when ax^2 + bx +1 is divided by x-2 is 9 It means that a(2)^2+2b+1 =9 or 4a+2b=8 or 2a+b=4 ----- (2) (1) + (2), we have 4a = 12, a=3 (and b= -2)
其他解答:
Let f(x)=x^2 + ax + b g(x)=ax^2 + bx +1 The remainder when x^2 + ax + b is divided by x+2 is -4 f(-2)= 4-2a+b=-4 -2a+b=-8 2a-b=8 ------------(*) The remainder when ax^2 + bx +1 is divided by x-2 is 9. The value of a is g(2) = 4a +2b+1 =9 4a +2b =8 2a +b =4 -------------(**) (**)-(*) 2b = -4 b=-2 From (**) 2a+(-2)=4 2a=4-(-2) 2a=4+2 2a=6 a=3
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