Let f(x)= 8x^3 + kx^2 +4(3x+1)
i) If x-2 is factor of f(x), find the value of k
ii) Find the roots of f(x) = 0 . (Leave yout answers in surd form id necessary.)
b) It is given that there are 10identical alloy cylinders with base radius r cm and height
1/7/6 cm.
i) If the ten cylinders are mlted and recast into two spheres with radii r cm and (r-1) cm , where r is an integer , find the valus of r.
Maths 高手請入
2007-04-14 8:57 am
回答 (2)
2007-04-14 1:07 pm
✔ 最佳答案
a) i) by Factor theorem, f(2) = 8*2^3 + k*2^2 + 4*(3*2+1) = 0
=> k = - [8*2^3 + 4*(3*2+1)] / 2^2 = -23
ii) f(x)= 8x^3 - 23x^2 + 12x+ 4
= (x - 2)(8x^2 - 7x - 2) = 0 (you may perform the long division)
x - 2 = 0 or 8x^2 - 7x - 2 = 0
x = 2 or [7 + sqrt(113)] / 16 or [7 - sqrt(113)] / 16
b) don't understand the following
It is given that there are 10identical alloy cylinders with base radius r cm and height
1/7/6 cm
2007-04-14 12:26 pm
f(x)= 8x^3 + kx^2 +4(3x+1)
i) f(2)=0
k=-23
ii)by long division , f(x)=(x-2)(8x^2-7x-2)
f(x)=0
x=2 or x= (7+(113)^1/2)/16 or x= -(7+(113)^1/2)/16
i) f(2)=0
k=-23
ii)by long division , f(x)=(x-2)(8x^2-7x-2)
f(x)=0
x=2 or x= (7+(113)^1/2)/16 or x= -(7+(113)^1/2)/16
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