There are at least two unequal real roots in the interval;

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