Conside a quadratic function f(x)=3x^2-9x+4and f(a)=f(b),where a=/=
a)find the value of a+b
b)hence find f(a+b)
ps 3x^2 =3x既2次 =/= 不等於
[f4 math] function問題
2006-10-24 4:26 am
回答 (2)
2006-10-24 4:31 am
✔ 最佳答案
Conside a quadratic function f(x)=3x^2-9x+4and f(a)=f(b),where a=/=a)find the value of a+b
f(a)=f(b)
3a^2-9a+4=3b^2-9b+4
3a^2-9a=3b^2-9b
3(a-b)(a+b)=9(a-b)
a+b=3 ( a=/=b)
b)hence find f(a+b)
f(a+b)
=f(3)
=3*3^2-9*3+4
=27-27+4
=4
2006-10-24 4:37 am
Conside a quadratic function f(x)=3x²-9x+4and f(a)=f(b),where a=/=
a)find the value of a+b
let a=0
f(0)=f(b)
3(0²)-9(0)+4=3b²-9b+4
4=3b²-9b+4
3b²-9b=0
b²-3b=0
b(b-3)=0
b=0(rejected because a≠b) or 3
so when a=0,b=3
a+b=3
b)hence find f(a+b)
f(a+b)=f(3)
=3(3²)-9(3)+4
=27-27+4
=4
a)find the value of a+b
let a=0
f(0)=f(b)
3(0²)-9(0)+4=3b²-9b+4
4=3b²-9b+4
3b²-9b=0
b²-3b=0
b(b-3)=0
b=0(rejected because a≠b) or 3
so when a=0,b=3
a+b=3
b)hence find f(a+b)
f(a+b)=f(3)
=3(3²)-9(3)+4
=27-27+4
=4
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