Q56 / 160 · TS EAMCET 2009 · Mathematics

If one of the roots of $\left|\begin{array}{lll}3 & 5 & x \\ 7 & x & 7 \\ x & 5 & 3\end{array}\right|=0$ is -10 , then the other roots are

  • Correct answer
    A
    3, 7
  • B
    4, 7
  • C
    3, 9
  • D
    3, 4

Solution

Given, $\left|\begin{array}{lll}3 & 5 & x \\ 7 & x & 7 \\ x & 5 & 3\end{array}\right|=0$ $\begin{array}{cc} \Rightarrow & 3(3 x-35)-5(21-7 x)+x\left(35-x^2\right)=0 \\ \Rightarrow & 9 x-105-105+35 x+35 x-x^3=0 \\ \Rightarrow & x^3-79 x+210=0 \\ \Rightarrow & (x+10)(x-3)(x-7)=0 \\ \Rightarrow & x=-10,3,7 \end{array}$

Hence, the correct answer is option: 'A'.

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