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You are given that the quadratic function is always negative, for all values of x.
It means that it has no real roots.
In turn, it means that the discriminant of this quadratic function is negative.
The discriminant of a quadratic function y = ax^2 + bx + c is
d = b^2 - 4ac.
In your case a= -3, b= k, c= -12, so the discriminant is
d = k^2 - 4*(-3)*(-12) = k^2 - 144.
You should determine "k" from this condition
d < 0, or k^2 - 144 < 0.
The solution is k^2 < 144, or -12 < k < 12.
ANSWER. The values of "k" are -12 < k < 12.
Solved.