The expression $4x^3+ax+b$, where $a$ and $b$ are constants, has a factor of $x-1$, and

Question

The expression $4x^3+ax+b$, where $a$ and $b$ are constants, has a factor of $x-1$, and a remainder of $-9$ when divided by $x+2$. Find the value of $a$ and of $b$.[4] Hence solve the equation $4x^3+ax+b=0$ expressing the non-integer roots in the form of $\frac{c+\sqrt{d}}{2}$, where $c$ and $d$ are constants.[4]

Accepted Answer

(a) $a=-9,\ b=5$ (b) $x=1$ or $x=\frac{-1\pm\sqrt{6}}{2}$

2025 AHS PRELIMS P2 Q2

2025 AHS PRELIMS P2 Q2

Solution:

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