Find the greatest integer value of b for which the expression 9x^3+4x^2+11x+7/x^2+bx+8 has a domain for all real numbers. Thank you!

Answer 1

the denominator cannot be zero. So,

x^2+bx+8 must have no real roots. For that to happen, we need the discriminant to be negative:

b^2-32 < 0
So |b| <= √32
5 is the greatest integer less than √32

Answer 2

The greatest integer is 5.
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