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!

Answer 1

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