The value of the determinant $\left|\begin{array}{lll}a^2 & a & 1 \\ b^2 & b & 1 \\ c^2 & c & 1\end{array}\right|$ is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $(a-b)(b-c)(a-c)$
$Δ=\left|\begin{array}{lll}a^2 & a & 1 \\ b^2 & b & 1 \\ c^2 & c & 1\end{array}\right|$
$R_3→R_3-R_2,R_2→R_2-R_1$
$\begin{vmatrix}a^2&a&1\\b^2-a^2&b-a&0\\c^2-b^2&c-b&0\end{vmatrix}$
$=(b^2-a^2)(c-b)-(c^2-b^2)(b-a)$
$(a^2-b^2)(b-c)-(a-b)(b^2-c^2)$
$-(a-b)(b-c)(-(a+b)+(b+c))$
$(a-b)(b-c)(a-c)$