數學inequality一問

第八題你注意第三步你乘左負一，大小符號要調轉

-4<x<4 or no real soln, or就係是但符合一個條件都得，咁就係-4<x<4，or all real no. 就係 all real no.

If the value of the quadratic equation y=(k-4)x^2-kx+4x+k-1 is non-negative for any real number x and k is an constant, find the range of values of k.

(k-4)x^2-kx+4x+k-1 >= 0 (non-negative)
(k-4)x^2+(4-k)x+(k-1) >= 0
delta <=0
(4-k)^2-4(k-4)(k-1) <=0
-3k(k-4)<=0
k(k-4)>=0
k<=0 or k>=4

45 - x^2 - 4x < 0

x^2 + 4x - 45 > 0

(x + 9)(x - 5) > 0

x < -9 or x > 5