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  • Explain Solution R.D. Sharma Class 12 Chapter deteminants Exercise 5.2 Question 52 sub question 4 maths Textbook Solution.

Explain Solution R.D. Sharma Class 12 Chapter  deteminants Exercise 5.2 Question 52 sub question 4 maths Textbook Solution.

Answers (1)

Answer: x=a, b

Hint Use determinant formula

Given:\left|\begin{array}{lll} 1 & x & x^{2} \\ 1 & a & a^{2} \\ 1 & b & b^{2} \end{array}\right|=0

Solution:

$$ L \cdot H S\left|\begin{array}{lll} 1 & x & x^{2} \\ 1 & a & a^{2} \\ 1 & b & b^{2} \end{array}\right|

$$ \begin{aligned} &\text { Apply } \mathrm{R}_{2} \rightarrow R_{2}-R_{1} \& R_{3} \rightarrow R_{3}-R_{1} \\ &\left|\begin{array}{ccc} 1 & x & x^{2} \\ 0 & a-x & a^{2}-x^{2} \\ 0 & b-x & b^{2}-x^{2} \end{array}\right| \end{aligned}

$$ \begin{aligned} &(a-x)(b-x) \text { common from } \mathrm{R}_{2} \& R_{3} \\ &=(a-x)(b-x)\left|\begin{array}{ccc} 1 & x & x^{2} \\ 0 & 1 & a+x \\ 0 & 1 & b+x \end{array}\right| \end{aligned}

Expand from C_{1}

\begin{aligned} &(a-x)(b-x)[b+x-a+x]=0 \\ &(a-x)(b-x)[-a+b]=0 \\ &a=x \\ &b=x \\ &a=b-\text { neglect } \end{aligned}

 

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