Determinant equation

Algebra Level 3

∣ x 3 2 0 3 1 7 3 x 20 17 1 1 1 ∣ = 0 \large \begin{vmatrix} x^3&20^3&17^3 \\ x&20&17 \\ 1&1&1 \end{vmatrix} = 0

Find the sum of all possible values of x x satisfy the equation above .


The answer is 0.

Tommy Li by Tommy Li , 22, Hong Kong

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1 solution

Genis Dude
Sep 2, 2017

When we open the determinant, we find that there are no x 2 x^2 term.Therefore the sum is 0 as the sum of roots of cubic equation is − x 2 c o e f f i c i e n t x 3 c o e f f i c i e n t -\frac {x^2 coefficient}{x^3 coefficient}

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