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  • Need solution for RD Sharma maths class 12 chapter 5 Determinants exercise multiple choise question 31

Need solution for RD Sharma maths class 12 chapter 5 Determinants exercise multiple choise question 31

Answers (1)

Answer:

Correct option (c)

Hint:

Simply solve the determinant and find  a.

Given:

Given that there are two values of a which makes the determinant.

        \Delta=\left|\begin{array}{ccc} 1 & -2 & 5 \\ 2 & a & -1 \\ 0 & 4 & 2 a \end{array}\right|=86

We have to find the sum of these two values of a.

Solution:

Here, we have

        \left|\begin{array}{ccc} 1 & -2 & 5 \\ 2 & a & -1 \\ 0 & 4 & 2 a \end{array}\right|=86

Expanding along R1, we get

        \begin{aligned} &\Rightarrow \quad 1\left(2 a^{2}+4\right)+2(4 a)+5(8-0)=86 \\ &\Rightarrow \quad 2 a^{2}+4+8 a+40=86 \\ &\Rightarrow \quad 2 a^{2}+8 a-42=0 \\ &\Rightarrow \quad a^{2}+4 a-21=0 \\ &\Rightarrow \quad(a+7)(a-3)=0 \\ &\Rightarrow \quad a=-7 \text { or } a=3 \end{aligned}

Hence sum of the two values of a = - 7 + 3 = -4.

Posted by

Gurleen Kaur

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