A. maths Inequalities (Ergent HW!!!!!!!!!!!!!!) 10pts
2007-10-20 5:29 am
For what values of k will the expression x^2-(k-4)x+k^2-5k+4 be non-negative for all real values of x?
回答 (2)
2007-10-20 5:39 am
✔ 最佳答案
For the expression be non- negative for all real values of x, x^2-(k-4)x+k^2-5k+4≧0, then
△≦0
[-(k-4)]^2-4(1)(k^2-5k+4)≦0
(k-4)^2-4(k-4)(k-1)≦0
(k-4)[(k-4)-4(k-1)]≦0
(k-4)(k-4-4k+4)≦0
(k-4)(-3k)≦0
(k-4)(3k)≧0
So k ≦ 0 or k ≧ 4
參考: My Maths Knowledge
2007-10-20 5:45 am
∵x^2-(k-4)x+k^2-5k+4 is non-negative for all real values of x
∴x^2-(k-4)x+k^2-5k+4≧0
x^2-(k-4)x+(k-4)(k-1)≧0
delta≦0
[-(k-4)]^2-4(k-4)(k-1)≦0
-3k(k-4)≦0
k(k-4)≧0
k≧4 or k≦0
∴x^2-(k-4)x+k^2-5k+4≧0
x^2-(k-4)x+(k-4)(k-1)≧0
delta≦0
[-(k-4)]^2-4(k-4)(k-1)≦0
-3k(k-4)≦0
k(k-4)≧0
k≧4 or k≦0
參考: King
收錄日期: 2021-04-13 14:01:34
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