(a)[4]
Determine the values of $a$ and $b$.
(b)[3]
Hence write $p(x)$ in factorised form.
(c)[2]
Find the smallest positive value of $\theta$ in radians for which $p(\cot 2\theta) = 0$.
Mathematics 9709 · AS & A Level · Trigonometry
Trigonometry — practice question
The polynomial $p(x)$ has the form $p(x) = ax^4 + bx^3 + 13x^2 - 35x + 15$, where $a$ and $b$ are constants. It is stated that $(2x - 1)$ and $(x - 3)$ are factors of $p(x)$.
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This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Substitute $x=\tfrac{1}{2}$ and $x=3$, then set each equal to zero to create two equations” …
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