Namely: x? +2x? +( 1-k)x=0
x(x? +2x+ 1-k)=0
Obviously there is a root x 1=0,
So, the equation: x? +2x+ 1-k=0 has at least one negative root.
In terms of function: k=x? +2x+ 1
Become a range problem, g(x)=x? +2x+ 1, when x < 0, g(x)≧0.
So, k≧0
That is, the minimum value of k is 0.
Have fun! I hope I can help you. If you don't understand, please ask. I wish you progress in your study! O(∩_∩)O