標題:
(Pure Mathematics) A question in pastpaper(2002) (40MARKS)
發問:
(a) Let f(x) = x3-3px+1 , where p∈R★ a(i)可以唔使做 (i) Show that f(x) = 0 has at least one real root.(ii) Using differentiation or otherwise, show that if p ≤ 0 , then f(x) = 0 has one only one root.(iii) If p > 0 find the range of values of p for each of the following cases :(1) f(x) = 0 has exactly one... 顯示更多 (a) Let f(x) = x3-3px+1 , where p∈R ★ a(i)可以唔使做 (i) Show that f(x) = 0 has at least one real root. (ii) Using differentiation or otherwise, show that if p ≤ 0 , then f(x) = 0 has one only one root. (iii) If p > 0 find the range of values of p for each of the following cases : (1) f(x) = 0 has exactly one real root (2) f(x) = 0 has exactly two distinct real root (3) f(x) = 0 has three distinct real root. 更新: (b) Let g(x) = x^4+4x+a , where a∈R (i) Prove that g(x) = 0 has at most two real roots. (ii) Prove that g(x) = 0 has two distinct real roots if and only if a is less than 3
(a) (ii) 圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Jan08/PP1.jpg (a) (iii) 圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Jan08/PP2.jpg (b) (i) 圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Jan08/PP3.jpg (b) (ii) 圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Jan08/PP4.jpg
其他解答:
(Pure Mathematics) A question in pastpaper(2002) (40MARKS)
發問:
(a) Let f(x) = x3-3px+1 , where p∈R★ a(i)可以唔使做 (i) Show that f(x) = 0 has at least one real root.(ii) Using differentiation or otherwise, show that if p ≤ 0 , then f(x) = 0 has one only one root.(iii) If p > 0 find the range of values of p for each of the following cases :(1) f(x) = 0 has exactly one... 顯示更多 (a) Let f(x) = x3-3px+1 , where p∈R ★ a(i)可以唔使做 (i) Show that f(x) = 0 has at least one real root. (ii) Using differentiation or otherwise, show that if p ≤ 0 , then f(x) = 0 has one only one root. (iii) If p > 0 find the range of values of p for each of the following cases : (1) f(x) = 0 has exactly one real root (2) f(x) = 0 has exactly two distinct real root (3) f(x) = 0 has three distinct real root. 更新: (b) Let g(x) = x^4+4x+a , where a∈R (i) Prove that g(x) = 0 has at most two real roots. (ii) Prove that g(x) = 0 has two distinct real roots if and only if a is less than 3
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最佳解答:(a) (ii) 圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Jan08/PP1.jpg (a) (iii) 圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Jan08/PP2.jpg (b) (i) 圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Jan08/PP3.jpg (b) (ii) 圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Jan08/PP4.jpg
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