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  • Please solve RD Sharma class 12 chapter Determinants exercise multiple choise question 5 maths textbook solution

Please solve RD Sharma class 12 chapter Determinants exercise multiple choise question 5 maths textbook solution

Answers (1)

Answer:

Correct option (d) none of these

Hint:

Simply solve the given determinant.

Given:

        \begin{vmatrix} x &2 &x \\ x^{2} &x &6 \\ x &x &6 \end{vmatrix}=ax^{4}+bx^{3}+cx^{2}+dx+e

We have to find value of 5a+4b+3c+2d+e.

Solution:

Here, taking L.H.S

        L.H.S=\begin{vmatrix} x &2 &x \\ x^{2} &x &6 \\ x &x &6 \end{vmatrix}

On solving determinant we have,

        =x(6x-6x)-2(6x^{2}-6x)+x(x^{3}-x^{2})

        =0-12x^{2}+12x+x^{4}-x^{3}

        =x^{4}-x^{3}-12x^{2}+12x

Comparing with R.H.S

        ax^{4}+bx^{3}+cx^{2}+dx+e

We get  a=1, b=-1,c=-12, d=12, e=0

    \Rightarrow    5a+4b+3c+2d+e=5(1)+4(-1)+3(-12)+2(12)+0

                                       =-11

Hence, option (d) is correct.

Posted by

Gurleen Kaur

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