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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Matrices
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If $\begin{vmatrix}x-1&5x&7\\x^2-1&x-1&8\\2x&3x&0\end{vmatrix}$ = $ax^3+bx^2+cx+d$ then $c$ is equal to

$(a)\;-1\qquad(b)\;12\qquad(c)\;15\qquad(d)\;17$

Can you answer this question?
 
 

1 Answer

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Given :
$\begin{vmatrix}x-1&5x&7\\x^2-1&x-1&8\\2x&3x&0\end{vmatrix}=ax^3+bx^2+cx+d$
LHS :
$(x-1)(0-24x)-5x(0-16x)+7(3x^3-3x-2x^2+2x)$
$\Rightarrow -24x^2+24x+80x^2+21x^3-14x^2-7x$
$\Rightarrow 21x^3+42x^2+17x$
$\Rightarrow 21x^3+42x^2+17x=ax^3+bx^2+cx+d$
$\Rightarrow c=17$
Hence (d) is the correct answer.
answered Nov 25, 2013 by sreemathi.v
 

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