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  • Please Solve R. D. Sharma class 12 Chapter determinants Exercise 5.2 Question 51 Maths textbook Solution.

Please Solve R. D. Sharma class 12 Chapter determinants Exercise  5.2 Question 51 Maths textbook Solution.

Answers (1)

Answer: $$ x=1,2,-3

Hint Use determinant formula

Given: $$ \text { S.T } x=2 \text { is root of equation }\left|\begin{array}{ccc} x & -6 & -1 \\ 2 & 3 x & x-3 \\ -3 & 2 x & x+3 \end{array}\right|=0

Solution:

$$ \left|\begin{array}{ccc} x & -6 & -1 \\ 2 & 3 x & x-3 \\ -3 & 2 x & x+3 \end{array}\right|=0

$$ \begin{aligned} &\text { Expand from } \mathrm{C}_{1}\\ &=x\left(-3 x^{2}-6 x-2 x^{2}+6 x\right)+(2 x+4+3 x-9)+30 x-30+5 x=0\\ &=-5 x^{2}+30 x-30+5 x=0\\ &=-5\left(x^{3}+7 x+6\right)=0\\ &=x^{3}+7 x+6=0\\ &=(x-1)\left(x^{2}+x-6\right)=0\\ &=(x-1)\left(x^{2}+3 x-2 x-6\right)=0\\ &=(x-1)(x+3)(x-2)=0\\ &x=1,2,-3 \end{aligned}

 

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