The equation whose roots are the negatives of the roots of the equation, $x^{7} + 3 x^{5} + x^{3} - x^{2} + 7 x + 2 = 0$ , is

x^{7} + 3 x^{5} + x^{3} - x^{2} - 7 x - 2 = 0

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x^{7} + 3 x^{5} + x^{3} + x^{2} + 7 x - 2 = 0

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x^{7} + 3 x^{5} + x^{3} - x^{2} - 7 x + 2 = 0

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x^{7} + 3 x^{5} + x^{3} - x^{2} + 7 x - 2 = 0

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Solution

The correct option is A $x^{7} + 3 x^{5} + x^{3} + x^{2} + 7 x - 2 = 0$
We get equation whose roots are negative of $x^{7} + 3 x^{5} + x^{3} - x^{2} + 7 x + 2 = 0$ by replacing $x \to - x$
${(- x)}^{7} + 3 {(- x)}^{5} + {(- x)}^{3} - {(- x)}^{2} + 7 (- x) + 2 = 0 \Rightarrow - x^{7} - 3 x^{5} - x^{3} - x^{2} - 7 x + 2 = 0 \Rightarrow x^{7} + 3 x^{5} + x^{3} + x^{2} + 7 x - 2 = 0$

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x^{7} + 3 x^{3} - 2 x^{3} + 7 x + 2 = 0

\int \frac{x^{7} + 2 x^{5} + x^{3} + 1}{x^{2} + 1} d x =

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α

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x_{3}, x_{4}, x_{5}, x_{6}

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x_{3} + x_{8} + x_{12} = - 11

x_{3} + x_{8} + x_{22} = ?

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