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Please solve RD Sharma class 12 chapter Determinants exercise multiple choise question 9 maths textbook solution

Answers (1)

Answer:

Correct option (b)

Hint:

Simply we will put x=0, then solve determinant.

Given:

Let

        \begin{vmatrix} x^{2}+3x &x-1 &x+3 \\ x+1 &-2x &x-4 \\ x-3 &x+4 &3x \end{vmatrix}=ax^{4}+bx^{3}+cx^{2}+dx+e

be an identity in x

Solution:

        \begin{vmatrix} x^{2}+3x &x-1 &x+3 \\ x+1 &-2x &x-4 \\ x-3 &x+4 &3x \end{vmatrix}=ax^{4}+bx^{3}+cx^{2}+dx+e

Putting x=0

        \Rightarrow \begin{vmatrix} 0 &-1 &3 \\ 1 &0 &-4 \\ -3 &4 &0 \end{vmatrix}=e

        \Rightarrow e=1(0-12)+3(4)

        \Rightarrow e=0

Hence, e=0 is correct answer.

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