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# Domain and Range

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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.

Feb 21, 2021

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$$x^2 + bx+ 8$$ = 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.

Feb 21, 2021