The polynomials $P(x)=ax^3+x^2+bx+10$ and $Q(x)=x^3+ax^2-5x+b$ leave the same remainder when div

Question

The polynomials $P(x)=ax^3+x^2+bx+10$ and $Q(x)=x^3+ax^2-5x+b$ leave the same remainder when divided by $x+2$. Show that $4a+b=4$.[2] If $P'(x)$ has a factor of $3x-2$, find the values of $a$ and $b$.[4] Solve the equation $2x^3+4x^2-5x-7=0$, expressing irrational roots in the form $a \pm \frac{1}{2}\sqrt{b}$ where $a$ and $b$ are constants to be determined.[5]

Accepted Answer

(a)(i) $4a+b=4$ (a)(ii) $a=2,\ b=-4$ (b) $x=-1,\ -\frac{1}{2}\pm\frac{1}{2}\sqrt{15}$

2025 CHS PRELIMS P2 Q4

2025 CHS PRELIMS P2 Q4

Solution:

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