(b) Find the remainder of f(x) is divided by x-3
更新1:
Why f*(2)=5 will be writed Let f*(x)=2ax+b
Pure Maths Polynomial
2010-10-19 4:52 am
(a) Find a polynomial f(x) of degree 2 such that f(1)=7 , f(2)=3 and f*(2)=5
(b) Find the remainder of f(x) is divided by x-3
(b) Find the remainder of f(x) is divided by x-3
回答 (2)
2010-10-19 5:10 am
✔ 最佳答案
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2010-10-18 21:11:01 補充：
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2010-10-18 22:22:23 補充：
I guess what you mean by f*(x) is the derivative of f(x)
2010-10-19 5:18 am
Sol
f(x)=a(x－1)(x－2)+b(x－1)+7
f(2)=b(1)+7=3
b=－4
f(x)=a(x－1)(x－2)－4(x－1)+7
=a(x^2－3x+2)－4x+11
=ax^2+(－3a－4)x+2a+11
f'(x)=2ax+(－3a－4)
f'(2)=4a－3a－4=a－4=5
a=9
f(x)=9x^2－31x+29
(b) Find the remainder of f(x) is divided by x－3
x－3=0
x=3
f(3)=81－93+29=17
f(x)=a(x－1)(x－2)+b(x－1)+7
f(2)=b(1)+7=3
b=－4
f(x)=a(x－1)(x－2)－4(x－1)+7
=a(x^2－3x+2)－4x+11
=ax^2+(－3a－4)x+2a+11
f'(x)=2ax+(－3a－4)
f'(2)=4a－3a－4=a－4=5
a=9
f(x)=9x^2－31x+29
(b) Find the remainder of f(x) is divided by x－3
x－3=0
x=3
f(3)=81－93+29=17
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