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Cubic equations: roots in arithmetic progression

mathematical

The equation

2x^3 - 9x^2 + kx - 6 = 0

has three real roots that form an arithmetic sequence.

Facts you may need

For $2x^3 - 9x^2 + kx - 6$ : sum of roots $= \frac92$ , product $= 3$ — Vieta's formulas.
Factor theorem — A known root gives a linear factor.

Find the value of

k

Find the three roots.