Find all values of the parameters a and b

Question

so that the following function has vertical asymptotes at x=1 and x=5 f(x)=(x+7)/(x^2 +ax +b)?

Answer 1

The rational function

Vertical asymptotes are found  by solving denominator = 0

We need to find quadratic function is y  = ax² + bx + c

Where a ,b ,c  are  parameters or coefficients of quadratic function.

In this case vertical asymptotes are x  = 1 and x  = 5

So the factoring of denominator is (x  - 1)(x  - 5)

x² - 5x - x + 5 

x² - 6x + 5 

y  = x² - 6x + 5 

Then the function is

 Compare it to

Therefore, a = - 6 and b = 5.