(a)[4]
Determine the value of $a$ and then factorise $p(x)$.
(b)[3]
Demonstrate that the equation $p(e^{3y}) = 0$ has just one real root and determine its exact value.
Mathematics 9709 · AS & A Level · Logarithmic and exponential functions
Logarithmic and exponential functions — practice question
The polynomial $p(x)$ is given by $p(x) = 2x^3 + ax^2 - 3x - 4$, with $a$ a constant. It is stated that $(x - 4)$ is a factor of $p(x)$.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Put in $x=4$, make the expression equal to zero and try to solve” …
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