Relation Between Roots and Coefficients for Higher Order Equations
For the equat...
Question
For the equation, x7+3x6−2x5+4x4−4x3+3x2−2x+1=0
, the value of the sum of the roots taken 3 at a time is:
A
−4
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B
4
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C
3
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D
−3
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Solution
The correct option is A−4 The given equation is x7+3x6−2x5+4x4−4x3+3x2−2x+1=0.
According to the relation between the roots and coefficients of an equation a0xn+a1xn−1+a2xn−2+...+an=0 with degree n, the sum of the roots taken r at a time is given by Sr=(−1)rara0. ⇒S3=−41=−4