For the equation, $7 x^{6} - 4 x^{5} + 3 x^{4} - 2 x + 9 = 0$ , if the sum of the roots taken two at a time is represented by $S_{2},$ then the value of $S_{2}$ is:

\frac{3}{7}

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\frac{- 2}{7}

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\frac{- 4}{7}

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\frac{4}{7}

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Solution

The correct option is A $\frac{3}{7}$
Given Equation: $7 x^{6} - 4 x^{5} + 3 x^{4} - 2 x + 9 = 0.$
This equation has a degree $6.$

For a equation of the form, $a_{0} x^{n} + a_{1} x^{n - 1} + a_{2} x^{n - 2} + . . . + a_{n} = 0,$
Sum of the roots taken $2$ at a time is given by $S_{2} = \frac{a_{2}}{a_{0}} = \frac{3}{7}$

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