Matrix Problem

[dusky hull]

2(a)

Is there any other way otherthan Compairing LHS and RHS expansions!?

[onyx raven]

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+close

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[wise dock]

Hmm... Kinda looks like the definition of the discriminant. Wonder if that can be exploited somehow.

[jolly flame]

,rotate

[dusky hull]

discriminant?
what's that ?

[jolly flame]

I assume this is lower case S?

$$ s_r = \alpha ^r + \beta ^r + \gamma ^r, r=0,1,2,3,4 $$

[severe ridge]

aL

[wise dock]

It's a function that's related to roots of a polynomial. It's defined like this.
Here n is the degree of the polynomial and a(n) is its leading coefficient.

[jolly flame]

write the determinant using 1st column for example, it's tedious but it works out

tedium can be reduced a little bit by using the row/column-additivity of the determinant