Find the greatest integer value of b for which the expression
(9x^3+4x^2+11x+7)/(x^2+bx+18)
has a domain of all real numbers.
+130118 We just need to make sure that x^2 + bx + 18 does not = 0
In other words, we need to have the discriminant of this function be < 0
So
b^2 - 4 (1) (18) < 0
b^2 - 72 < 0
b^2 < 72
This will be true for the integer values on [ -8, 8 ]
So b = 8 is the largest integer value of b that will give us a domain of all reals
