Suppose a cubic polynomial f(x) has three real roots a, b, and c which are not all equal.

Given the slopes of the tangent lines at two of these roots, find the slope of the third.

In other words, if f'(a)=p and f'(b)=q (where p and q are not both 0), find a formula for f'(c) in terms of p and q.

Posted by K Sengupta on 2022-06-27 01:52:07