Consider an equation x 4 + a x 3 + b x 2 + c x + d = 0 with roots (of x ) x 1 , x 2 , x 3 and x 4 . If x 1 2 0 1 6 + x 2 2 0 1 6 + x 3 2 0 1 6 + x 4 2 0 1 6 = 4 , find the maximum value of a , a max .
Submit your answer as a max + b + c + d + x 1 + x 2 + x 3 + x 4 when a max is fulfilled.
Set .
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@shubham poddar How can you say this that all roots MUST be equal to -1 ??? Show your working!!!
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For maximum a, all the roots must be equal to -1. Hence a=4, b=6, c=4, d=1, x1=-1, x2=-1, x3=-1,x4=-1 Hence the ans is 4+6+4+1-1-1-1-1=11.