(a)[2]
Determine the value of $a$.
(b)[3]
With this value of $a$, factorise $p(x)$ completely.
(c)[4]
Hence find the exact values of $y$ for which $p(e^{y} + e^{-y}) = 0$.
Mathematics 9709 · AS & A Level · Logarithmic and exponential functions
Logarithmic and exponential functions — practice question
The polynomial $p(x)$ is defined as $p(x) = ax^3 - 11x^2 - 19x - a$, where $a$ is a constant. It is known that $(x - 3)$ is a factor of $p(x)$.