(a)[5]
Determine the values of $a$ and $b$.
(b)[5]
Hence determine the exact root of the equation $p(e^{2y}) = 0$.
Mathematics 9709 · AS & A Level · Logarithmic and exponential functions
Logarithmic and exponential functions — practice question
The polynomial $p(x)$ is given by $p(x)=x^3+ax+b$, with $a$ and $b$ as constants. You are told that $(x+2)$ is a factor of $p(x)$ and that, on dividing $p(x)$ by $(x-3)$, the remainder is $5$.