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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