Asked by Trish Goal

Find the greatest integer value of b for which the expression 9x^2+4x^2+11x+7/x^2+bx+8 has a domain for all real numbers? Thank you!
Answered by Steve
if the domain is all real numbers then the denominator can never be zero. That means it has no real roots. Thus, the discriminant is negative:

b^2-32 < 0
So, if 0<=b<=5 x^2+bx+8 is never zero