Mathematics 9709 · AS & A Level · Logarithmic and exponential functions
Logarithmic and exponential functions — practice question
The polynomial $p(x)$ is given by $p(x) = ax^3 + 3x^2 + 4ax - 5$, where $a$ is a constant. It is stated that $(2x - 1)$ is a factor of $p(x)$.
(i)[2]
Apply the factor theorem to determine the value of $a$.
(ii)[4]
Factorise $p(x)$ and hence demonstrate that the equation $p(x) = 0$ has just one real root.
(iii)[2]
Use logarithms to solve the equation $p(6^y) = 0$ correct to $3$ significant figures.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Put $x = \tfrac{1}{2}$ and set the expression equal to zero” …