Quote (Forg0tten @ May 19 2017 09:41am)
Didn't want to open a new thread haha
I once already got an answer for this very question, however, I forgot how to solve it. Besides, somebody gave me one explanation that I can't keep up with but he hasn't been back on forum since giving the explanation.
f(x) = x^3 - 11x^2 - 25x - 13
y = p*x + q
Line Y is the tangent of f(x) at A(a,f(a)) and intersects with f(x) at B (13,0). What is the sum of p+q?
Code
So I suppose this means that For A, f(a) = y(a) ∧ f ' (a) = y' (a)
Furthermore, 0 = 13p+q --> q = -13p --> y = p*x-13p = p(x-13)
Consider this for f(a)=y(a) --> f(a)-y(a)=0 --> x^3 - 11x^2 - 25x - 13 -p(x-13) = 0
I can sense the possibility of grouping here, which is precisely the explanation I had on the other forum (see quote)
I don't understand just how to factorize this problem. Can anybody tell me what tool I need to do this? I'll be happy to look it up myself from there.
/e Is there a way for me to assume that A and B are the only solutions? If so, one can assume that there has to be a factor (x-13).
I hate having to double post, but I couldn't edit anymore.
What I did was,
if one factor is (x-13) then (x-13)(ax^2 + bx + c) = x^3 - 11x^2 - (p+25)x - 13+13p
Where a must equal 1 and c must equal 13+13p
If at some point I can assume that this only has one solution, I know that x = -b +-Sqrt(b^2-4ac)/2a and this will lead to p=0
But this leans strongly on the assumption that there are no other solutions. Does tangent at A and intersect at B between a linear equation and a cubic equation mean that there is no other point of interaction between the two equations?
This post was edited by Forg0tten on May 19 2017 03:50am