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Answer: \(x = \frac{\sqrt{2}}{\sqrt{3}}\) (both roots equal)

Product \(3\times 2 = 6\), sum \(-2\sqrt{6}\): use \(-\sqrt{6}\) and \(-\sqrt{6}\). Note \(\sqrt{6} = \sqrt{3}\cdot\sqrt{2}\) and \(3 = \sqrt{3}\cdot\sqrt{3}\).

\[3x^2 - \sqrt{6}x - \sqrt{6}x + 2 = 0\]\[\sqrt{3}x(\sqrt{3}x - \sqrt{2}) - \sqrt{2}(\sqrt{3}x - \sqrt{2}) = 0\]\[(\sqrt{3}x - \sqrt{2})^2 = 0\]

So \(\sqrt{3}x = \sqrt{2}\), i.e. \(x = \frac{\sqrt{2}}{\sqrt{3}}\), and both roots are equal.

Doubtly AI · 24 Oct 2026 AI-verified · Oct 2026 Report
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