Question 12

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Jambmaths question: 

if (x – 1), (x + 1) and (x – 2) are factors of the polynomial $a{{x}^{3}}+b{{x}^{2}}+cx-1$. Find a b c respectively 

Option A: 

$-\tfrac{1}{2},1,\tfrac{1}{2}$

Option B: 

$\tfrac{1}{2},1,\tfrac{1}{2}\text{ }$

Option C: 

$\tfrac{1}{2},1,-\tfrac{1}{2}$

Option D: 

$\tfrac{1}{2},-1,\tfrac{1}{2}$

Jamb Maths Solution: 

$\begin{align}  & (x-1)(x+1)(x-2)=({{x}^{2}}-1)(x-2) \\ & \text{                             }={{x}^{3}}-2{{x}^{2}}-x+2 \\ & \text{Divide the expression (}{{x}^{3}}-2{{x}^{2}}-x+2\text{) through by }-2 \\ & \text{The new expression will be }-\frac{{{x}^{3}}}{2}+{{x}^{2}}+\frac{x}{2}-1 \\ & \text{Comparing the expression }-\frac{{{x}^{3}}}{2}+{{x}^{2}}+\frac{x}{2}-1\text{ with } \\ & a{{x}^{3}}+b{{x}^{2}}+cx-1\text{ gives }a=-\tfrac{1}{2}\text{ }b=+1,\text{ }c=+\tfrac{1}{2} \\\end{align}$

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