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.

Related questions
Impact of this question
663 views around the world
You can reuse this answer
Creative Commons License