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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.

 Feb 15, 2024
 #1
avatar+128732 
+2

This will have a domain of  all real numbers if  the discriminant of the quadratic in the  denominator is < 0

 

So

 

b^2  - 4*18 < 0

 

b^2  - 72 < 0

 

b^2  < 72

 

b =  8

 

cool cool cool

 Feb 15, 2024

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