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99. stam of roots of the equation \( \frac{3 x^{3}-x^{2}+x-1}{3 x^{3}-x^{2}-x+1}=\frac{4 x^{3}+7 x^{2}+x+1}{4 x^{3}+7 x^{2}-x-1} \) is :(A) 0(B) 1(C) - 1(D) 2 |
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Answer» \(\frac{3x^3 - x^2 + x - 1}{3x^3 - x^2 - x + 1}\) \(= \frac{4x^3 + 7x^2 + x + 1}{4x^3 + 7x^2 - x - 1}\) \(\Rightarrow\) \((3x^3 - x^2 + x - 1)\) \((4x^3 + 7x^2 - x - 1)\) \(= (4x^3 + 7x^2 + x + 1)\) \((3x^3 - x^2 - x + 1)\) \(\Rightarrow\) \(12x^6 + 17x^5 - 6x^4\) \(+\, x^3 - 7x^2 + 1\) \(= 12x^6 + 17x^5 - 8x^4\) \(-\, x^3 + 5x^2 + 1\) \(\Rightarrow\) \(8x^4 - 6x^4 + x^3 + x^3\) \(-\, 7x^2 - 5x^2 + 1 - 1 = 0\) \(\Rightarrow\) \(2x^4 + 2x^3 - 12x^2 = 0\) \(\Rightarrow\) \(x^4 + x^3 - 6x^2 = 0\) \(\therefore\) sum of roots \(= \frac{-\text{Coefficient of}\,x^3}{\text{Coefficient of}\,x^4}\) \(= \frac{-1}{1} = -1.\) |
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