Extraordinary Polynomial

Algebra Level 4

a x 3 + b x 2 + c x + d ax^3+bx^{2}+cx+d is a cubic polynomial,

where ( a , b , c , d ) ϵ N (a,b,c,d)\epsilon N

has real roots x 1 , x 2 , x 3 x_{1},x_{2},x_{3}

such that ,

f ( 2 ) = 140 f(2)=140

f ( 3 ) = 240 f(3)=240

f ( 5 ) = 560 f(5)=560

f ( 7 ) = 1080 f(7)=1080

Then evaluate ,

( i = 1 3 2 + x i ) + ( i = 1 3 3 + x i ) + ( i = 1 3 5 + x i ) (\sum_{i=1}^{3}2+x_{i}) + (\sum_{i=1}^{3}3+x_{i})+(\sum_{i=1}^{3}5+x_{i})


The answer is 0.

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1 solution

Aareyan Manzoor
Nov 14, 2015

solve simultinious eqns by subtracting the nth line from the n+1 line and multiplying/ dividing to make elimination easiear by vietas we are looking for which is 30-30= 0 \boxed{0}

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