Question 288830
Vertical asymptotes of rational functions occur for values of x that make the denominator zero (if any). To find them then, set the denominator equal to zero and solve:
{{{x^2+2x-25 = 0}}}
This will not factor so I'll use the quadratic formula:
{{{x = (-b +- sqrt(b^2 -4ac))/(2a)}}}
{{{x = (-(-2) +- sqrt((-2)^2 -4(1)(-25)))/(2(1))}}}
{{{x = (2 +- sqrt(4 -4(1)(-25)))/2}}}
{{{x = (2 +- sqrt(4 + 100))/2}}}
{{{x = (2 +- sqrt(104))/2}}}
{{{x = (2 +- sqrt(4*26))/2}}}
{{{x = (2 +- sqrt(4)*sqrt(26))/2}}}
{{{x = (2 +- 2*sqrt(26))/2}}}
{{{x = (2(1 +- sqrt(26)))/2}}}
{{{x = (cross(2)(1 +- sqrt(26)))/cross(2)}}}
{{{x = 1 +- sqrt(26))}}}
So there will be two vertical asymptotes:
{{{x = 1 + sqrt(26))}}}
and
{{{x = 1 - sqrt(26))}}}