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.
+208 If \(\frac{9x^3\:+\:4x^2\:+\:11x\:+\:7}{x^2\:+\:bx\:+\:18\:}\) is real, its denominator must never equal zero
The discriminant of x^2+bx+18 is b^2-72
if x^2+bx+18 doesn't equal zero, than:
b^2-72<0
b=+/-(6 sqrt (2))
so the greatest integer is 8
JP
+208 If \(\frac{9x^3\:+\:4x^2\:+\:11x\:+\:7}{x^2\:+\:bx\:+\:18\:}\) is real, its denominator must never equal zero
The discriminant of x^2+bx+18 is b^2-72
if x^2+bx+18 doesn't equal zero, than:
b^2-72<0
b=+/-(6 sqrt (2))
so the greatest integer is 8
JP
