If Delta=left|begin{array}{lll}1 & a & a^2 1 | vedclass

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(B) Given the determinant $\Delta = \begin{vmatrix} 1 & a & a^2 \ 1 & b & b^2 \ 1 & c & c^2 \end{vmatrix}$.Applying row operations $R_1 	o R_1 - R_

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(B) Given the determinant $\Delta = \begin{vmatrix} 1 & a & a^2 \ 1 & b & b^2 \ 1 & c & c^2 \end{vmatrix}$.Applying row operations $R_1 	o R_1 - R_2$ and $R_2 	o R_2 - R_3$:$\Delta = \begin{vmatrix} 0 & a-b & a^2-b^2 \ 0 & b-c & b^2-c^2 \ 1 & c & c^2 \end{vmatrix}$Taking $(a-b)$ common from $R_1$ and $(b-c)$ common from $R_2$:$\Delta = (a-b)(b-c) \begin{vmatrix} 0 & 1 & a+b \ 0 & 1 & b+c \ 1 & c & c^2 \end{vmatrix}$Expanding along $C_1$:$\Delta = (a-b)(b-c) [1 \cdot ((b+c) - (a+b))]$$\Delta = (a-b)(b-c)(c-a)$Comparing this with $K(a-b)(b-c)(c-a)$, we get $K = 1$.

If $\Delta=\left|\begin{array}{lll}1 & a & a^2 \\ 1 & b & b^2 \\ 1 & c & c^2\end{array}\right|=K(a-b)(b-c)(c-a)$, then $K=$

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