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given that all roots are non-negative real numbers.

February 22, 2026

given that all roots are non-negative real numbers.

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oxed{-2u + 10}
Compute the sum of the roots of the equation
\[ u\sqrt{u} - 5u + 6\sqrt{u} - 4 = 0 \]
Let \( x = \sqrt{u} \), so \( u = x^2 \) and \( u\sqrt{u} = x^2 \cdot x = x^3 \). Substitute:
\[ x^3 - 5x^2 + 6x - 4 = 0 \]
We solve this cubic equation. Try rational roots: \( \pm1, \pm2, \pm4 \).

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