F4 Math一問~~~~~
2007-10-05 3:37 am
If f (x) = x^2 +ax+b , and f ( -1 ) =0 and f( 1 )= -4 , find the value of a and b .
回答 (2)
2007-10-05 3:40 am
✔ 最佳答案
f(-1)=0(-1)^2+a(-1)+b=0
1-a+b=0
-a+b=-1---(1)
f(1)=-4
(1)^2+a(1)+b=-4
1+a+b=-4
a+b=-5----(2)
(1)-(2)
-2a=-6
a=3
Put a=3 into(2)
3+b=-5
b=-8
2007-10-05 3:46 am
f ( -1 ) =0
(-1)^2 + a(-1)+b = 0
1-a+b=0
b=a-1 ---------------------------------(*)
f(1)= (1)^2+a(1)+b = -4
1+a+b = -4
a+b = -5
put (*) into it,
a+ (a-1) = -5
2a-1 = -5
a = -2
put a = -2 into (*)
b = (-2) - 1
b = -3
(-1)^2 + a(-1)+b = 0
1-a+b=0
b=a-1 ---------------------------------(*)
f(1)= (1)^2+a(1)+b = -4
1+a+b = -4
a+b = -5
put (*) into it,
a+ (a-1) = -5
2a-1 = -5
a = -2
put a = -2 into (*)
b = (-2) - 1
b = -3
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