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.


I know the interval notation, but how would you solve for \(b?\)



ant101  Nov 29, 2018

We only need to worry about the denominator  being 0


We need to find  the largest "b" that would give no real roots to the polynomial in the denominator


To do this....set the discriminant  = 0


b^2 - 4(1)(8)  = 0


b^2 - 32 = 32


b^2  = 32


Take the square root and b ≈ 5.66


This means that if b = 5, we will have no real zeros in the denominator because the discriminant will be < 0


So....the greatest integer value of b   = 5     


To get a feel for this look at the graphs of  x^2 + 6x + 8  and x^2 + 5x + 8




Note that the first will have real zeros, but the second will not since it never intersects the x axis



cool cool cool

CPhill  Nov 29, 2018

Oh, I get it! Just have to look at the denominator! Thank you, CPhill! 

ant101  Nov 29, 2018

23 Online Users


New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.