Domain and Range

Question

+1

477

1

+148

Find the greatest integer value of $b$ for which the expression $\frac{9x^3+4x^2+11x+7}{x^2+bx+8}$ has a domain of all real numbers.

powclaire Feb 21, 2021

CubeyThePenguin · Answer 1 · 2021-02-21T01:54:37

$x^2 + bx+ 8$ = 0 has to have no real solutions. So, the discriminant neds to be less than 0.

$\Delta = b^2 - 4ac= b^2 - 32 < 0$

$b^2 < 32$

The greatest integer value of b is 5.