It is given that $\mathrm{f}(x) = 3x^3 + ax^2 - 7x + 3$, where $a$ is a constant, has

Question

It is given that $\mathrm{f}(x) = 3x^3 + ax^2 - 7x + 3$, where $a$ is a constant, has a factor of $x + 1$. Find the value of $a$ and factorise $\mathrm{f}(x)$ completely.[4] Solve the equation $\mathrm{f}(\cot^2 \theta) = 0$ for $-90{}^\circ < \theta < 90{}^\circ$.[3]

Accepted Answer

(a) $a=-7$, $f(x)=(x+1)(3x-1)(x-3)$ (b) $\theta=-60^\circ,-30^\circ,30^\circ,60^\circ$

(A Math) 2025 CCHY PRELIMS P2 Q4

(A Math) 2025 CCHY PRELIMS P2 Q4

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