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Maths-

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Easy

Question

The condition for the expression ax² + 2hxy + by² + 2gx + 2fy + c to be resolved into rational linear factors in the determinant form is -

$|\begin{matrix} a & b & c \\ h & g & f \\ 1 & 1 & 1 \end{matrix}|$ = 0
$|\begin{matrix} a & h & f \\ h & b & g \\ f & g & c \end{matrix}|$ = 0
$|\begin{matrix} a & h & g \\ h & b & f \\ g & f & c \end{matrix}|$ = 0
None of these

The correct answer is: $open vertical bar table row a h g row h b f row g f c end table close vertical bar$ = 0

Step by step solution:
The condition for the expression ax2 + 2hxy + by2 + 2gx + 2fy + c to be resolved into rational linear factors in the determinant form is:
$open vertical bar table row a h g row h b f row g f c end table close vertical bar equals 0$
Hence, option(d) is the correct option.

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