Sum of the roots
Let P(x)= x 2 0 − 2 x 1 9 + 4 x 1 8 − 8 x 1 7 . . . . . . + 2 2 0 x − 2 2 1 . Find the sum of the roots of P(x).
The answer is 2.
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3 solutions
- By Girard´s relationships we know that the sum of the roots is: a − b .
- So the sum will be 1 − ( − 2 ) = 2.
By vietes formulas we get − ( y 0 + y 1 + y 2 + ⋯ + y 1 9 ) = − 2 where y n are the roots Simpifying we get y 0 + y 1 + y 2 + ⋯ + y 1 9 = 2
sum of root of n degree polynomial = - coeff. of x^n-1 / coeff. of x^n. answer = -(-2)/1 = 2