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?
how did u get those intervals?
What i had done was that I had differentiated the function and got the points where slope is zero as x=10/3 and x=0.
At x=0 the function takes the value 2
and at x=10/3 the function takes the value -16.518.
So, there must exist atleast one real root where the functions value is 0.
Any input will be appreciated.