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Let x, y, z be positive reals and D be the determinant with rows (x, x³, x⁴ - 1), (y, y³, y⁴ - 1), (z, z³, z⁴ - 1). If x, y, z are the roots of t³ - 21 t² + b t - 343 = 0 (b real), then D equals
- 1
- 0
- dependent on x, y, z
- data inadequate
Correct answer: dependent on x, y, z
Solution
D factors as -(x-y)(x-z)(y-z)[xyz(xy+yz+zx) - (x+y+z)] = -(x-y)(x-z)(y-z)(343b - 21); since the roots are not uniquely determined by b, D depends on x, y, z.
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