If in the given equation, #ax^3+bx^2+cx+d=0# has roots #alpha,beta,gamma#.Then what is the value of #(α^2)β - (α^2)γ + (β^2)γ - (β^2)α + (γ^2)α - (γ^2)beta#?

1 Answer
George C.
Jan 6, 2018

The conditions are insufficient to determine the value.

Explanation:

The value of:

#alpha^2beta-alpha^2gamma+beta^2gamma-beta^2alpha+gamma^2alpha-gamma^2beta#

is not determined by the given conditions.

To see this, note that if we swap #beta# and #gamma# then the sign of the value is inverted, yet to say that #alpha, beta, gamma# are the roots of the cubic equation does not determine their order.

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