(i)[5]
Find the values for $a$ and $b$.
(ii(a))[4]
Show that $p(x)=0$ has precisely one real root.
(ii(b))[3]
Solve $p(\sec y) = 0$ when $-180^{\circ} < y < 180^{\circ}$.
Mathematics 9709 · AS & A Level · Trigonometry
Trigonometry — practice question
The polynomial $p(x)$ is given by $p(x) = ax^3 + 3x^2 + bx + 12$, with $a$ and $b$ as constants. It is stated that $(x + 3)$ is a factor of $p(x)$, and that the remainder when $p(x)$ is divided by $(x + 2)$ is $18$.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Set $x=-3$, make the expression equal to zero and arrive at $27a+3b=39$ or equivalent” …
- Full mark scheme, point by point
- Step-by-step worked solution
- Write your answer & get it marked instantly by AI