The polynomial $\mathrm{f}(x)$ is such that $\mathrm{f}(x) = 6x^3 + ax^2 - 50x + b$, where&

Question

The polynomial $\mathrm{f}(x)$ is such that $\mathrm{f}(x) = 6x^3 + ax^2 - 50x + b$, where $a$ and $b$ are integers. It is given that $\mathrm{f}(x)$ is divisible by $2x - 3$ and that $\mathrm{f}'(1) = 6$. Find the values of $a$ and $b$.[5] Using your values of $a$ and $b$, solve the equation $\mathrm{f}(x) = 0$.[3]

Accepted Answer

(a) $a=19$, $b=12$ (b) $x=\frac32,\ \frac{-7+\sqrt{61}}3,\ \frac{-7-\sqrt{61}}3$

2024 FMSS PRELIMS P1 Q7

2024 FMSS PRELIMS P1 Q7

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