If $f(x) = \left| \begin{matrix} 1 + a & 1 + ax & 1 + ax^{2} \ 1 + b & 1 + bx & 1 + {bx}^{2} \ 1 + c & 1 + cx & 1 + {cx}^{2} \end{matrix} ight|,\$where $a,b,c$ are non-zero constants, then value of $f(10)$is

Question

If $f(x) = \left| \begin{matrix} 1 + a & 1 + ax & 1 + ax^{2} \ 1 + b & 1 + bx & 1 + {bx}^{2} \ 1 + c & 1 + cx & 1 + {cx}^{2} \end{matrix} ight|,\$where $a,b,c$ are non-zero constants, then value of $f(10)$is

Dr. Abubacker · Accepted Answer

(d)
Given, $f(x) = \left| \begin{matrix}
1 + a & 1 + ax & 1 + ax^{2} \
1 + b & 1 + bx & 1 + {bx}^{2} \
1 + b & 1 + cx & 1 + {cx}^{2}
\end{matrix} ight|$
$\Rightarrow f(x) = \left| \begin{matrix}
1 + a & a(x - 1) & ax(x - 1) \
1 + b & b(x - 1) & bx(x - 1) \
1 + b & c(x - 1) & cx(x - 1)
\end{matrix} ight|$
$= (x - 1)x(x - 1)\left| \begin{array}{r}
1 + a\ \ a\ \ a \
1 + b\ \ b\ \ b \
1 + c\ \ c\ \ c
\end{array} ight|$=0
($	herefore two\ columns\ are\ same)$

Q. If $f(x) = \left| \begin{matrix} 1 + a & 1 + ax & 1 + ax^{2} \\ 1 + b & 1 + bx & 1 + {bx}^{2} \\ 1 + c & 1 + cx & 1 + {cx}^{2} \end{matrix} \right|,\$where $a,b,c$ are non-zero constants, then value of $f(10)$is

Explanation

Reviewed by Dr. Abubacker

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