How do you solve #-2x^2+6X+15 <=0#?
Half closed intervals: (-inf., x2] and [x1, inf.)
First, solve f(x) = 0 to find the 2 real roots. Use the improved quadratic formula (Socratic Search)
There are 2 real roots (2 x-intercepts):
Since a < 0, the parabola opens downward.
f(x) > 0 inside the interval (x2, x1), between the 2 x-intercepts.
f(x) < 0 outside the (x2, x1) interval, because the 2 parabola branches are below the x-axis.
Solution set: Two half-closed intervals (-inf., x2] and [x1, inf.)
The 2 end points x1 and x2 are include in the solution set