(5-k)x^2 + (k-10)x + (k+5) >= 0 , which is a quadratic equation in x.
For a quadratic curve lies above or touches the x-axis, the quadratic equation must have 1 real root or 0 real root. Therefore, the leading coefficient must be positive and its discriminant must be non-positive.
Hence, from the given conditions, we require k>0 and 5-k>0 and discriminant <=0 i.e. 0<k<5 and (k-10)^2-4(5-k)(k+5) <=0 etc.
之後自己solve吧 0 < k =< 4 成題數關鍵在於 g(x)-f(x)都係一條quadratic curve