I am asked to solve the parametric inequality and to find for which values of a every x is a solution.
$$ (a+5)x^2 - 2x(a+1) + 2a - 4 \ge 0 $$
So in order every x to be a solution to the inequality we need the discriminant $ \le 0$.
So I get $ -4a^2 - 16a + 84 \le 0 $
When I solve it I get that $x \le -7 \cup x \ge 3 $
The problem comes from the fact that in the solutions of the exercise it shows only $ x \ge 3 $
Why is that ? Am I missing something ? I think for all 10 exercises its showing only 1 root.
Hint: The discriminant being negative only tells you whether the graph lies completely above or completely below the x axis. You need more conditions to check for it being completely above..