The internal pressure P P\,P of a experimental gas chamber is modeled by the function:
P(v)=3v3+13v2+19v+kP(v) = 3v^3 + 13v^2 + 19v + kP(v)=3v3+13v2+19v+k
where v v\,v is the relative volume and k k\,k is a constant.
Given that (3v+1)(3v + 1)(3v+1) is a factor of P(v)P(v)P(v),
use the factor theorem to show that k=5k = 5k=5.
Hence show that the equation P(v)=0P(v) = 0P(v)=0 has only one real root.
Practise Edexcel A Level Maths 1.5 Algebraic Division with exam-style questions for A Level Maths. 65 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.