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How to solve this problem- - Complex numbers and quadratic equations - JEE Main-7

If B=\begin{bmatrix} 5 &2\alpha &1 \\ 0 &2 &1 \\ \alpha &3 &-1 \end{bmatrix} is the inverse of a 3\times 3 matrix A, then the sum of all values of \alpha for which det \left ( A \right )+1=0, is : 

 

 

 

 

  • Option 1)

    0

  • Option 2)

    1

  • Option 3)

    2

  • Option 4)

    -1

 
Answers (1)
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V Vakul

B=\begin{bmatrix} 5 &2\alpha &1 \\ 0 &2 &1 \\ \alpha & 3 &-1 \end{bmatrix}

\left | B \right |=5\left ( -5 \right )-2\alpha \left ( -\alpha \right )-2\alpha

        =2\alpha ^{2}-2\alpha -25

1+\left | A \right |=2\alpha ^{2}-2\alpha -25+1=0

                =2\alpha ^{2}-2\alpha -24=0

                =\alpha ^{2}-\alpha -12=0

                =\alpha ^{2}-4\alpha +3\alpha -12=0

                =\left ( \alpha -4 \right )\left ( \alpha +3 \right )=0

root=4,-3

sum\: \: of\: \: root=4-3

                              =1

 


Option 1)

0

Option 2)

1

Option 3)

2

Option 4)

-1

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