Consider the determinant = vmatrix a_1 + b_1 x^2 & a_1 x^2 + b_1 & c_1 a_2 + b_2 x^2…

MATHEMATICS · Subjective · CBSE · Mathematics · Determinants · Determinants

Problem

Consider the determinant

\Delta = \begin{vmatrix} a_1 + b_1 x^2 & a_1 x^2 + b_1 & c_1 \\ a_2 + b_2 x^2 & a_2 x^2 + b_2 & c_2 \\ a_3 + b_3 x^2 & a_3 x^2 + b_3 & c_3 \end{vmatrix} = 0,

where

a_i, b_i, c_i \in R (i = 1, 2, 3)

and

x \in R

Statement-1 The value of

x

satisfying

\Delta = 0

are

x = 1, -1

Statement-2 If

\begin{vmatrix} a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3 \end{vmatrix} = 0

, then

\Delta = 0