Let f(x) = (2x^2 + x + 5)/(x^2 + 6x + c).
Find the smallest integer value of c so that f(x) has a domain of all real numbers.
+128408 The numerator is defined for all real numbers
We need to have complex roots for the polynomial in the denominator
This will happen when the discriminant is < 0 ....so....
6^2 - 4c < 0
36 - 4c < 0
36 < 4c
9 < c means the same thing as c < 9
So....when c = 10, this rational function will have a domain of all reals
See the graph here to confirm this : https://www.desmos.com/calculator/mkpngao0r3
