1. Given a quadratic function f(x) = (k - 1)x^2 - 5(k - 1)x + 5k , where k is a constant.
a) State two inequalities for k such that f(x) > 0 or = 0 for any real number x . Hence , find the range of k. (唔洗呢條..)
b) if f(x) = 0 has double roots , solve for x. (答呢條!!)
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2007-12-07 9:36 pm
回答 (1)
2007-12-07 9:50 pm
✔ 最佳答案
1b) f(x) = (k - 1)x^2 - 5(k - 1)x + 5kΔ =0
[-5(k-1)]²-4(k-1)(5k) = 0
25(k²-2k+1)-20k(k-1) = 0
5k²-10k+5-4k²+4k = 0
k²-6k+5 = 0
(k-5)(k-1) = 0
k = 1(rejected,∵when k=1,f(x) isn't a quadratic function ) or 5 when f(x) has doble roots
for k=5
f(x) = 4x²-20x+25
0 = (2x-5)²
x = 5/2
收錄日期: 2021-04-13 14:39:51
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