Third degree polynomial equations
I am stuck on a problem :
[ x^3 + 7 ] / [x^2 + 1 ] = 5
Question is : How many real roots does this equation have?
IN this I cant use a graphing calculator. Nor do i have access to even a simple calculator.
I think this can be done using the Intermediate value theorm (if the value of the function is positive and negative for some values of x then it must pass through X axis because it is continous.) But this does not seem a very scientific method to me. Moreover, this is hit and try.
Any "proper" method to solve such questions?