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There are two values of x for which the determinant of the matrix [[1, -2, 5], [2, x, -1], [0, 4, 2x]] equals 86. What is the sum of these two values of x?

1. -4
2. 5
3. -3
4. 9

Correct answer: -4

Solution

Expanding gives 2x² + 8x - 4 - (some terms) = 86, a quadratic in x whose two roots sum to -4 by Vieta's formula.

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