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Home » The LCM is found by taking the highest power of all prime factors: - Carbonext

The LCM is found by taking the highest power of all prime factors: - Carbonext

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Question: Compute the sum of the roots of the equation

📌 u\sqrt{u} - 6u + 7\sqrt{u} - 12 = 0,

📌 given that all roots are real and non-negative.

📌 Solution: Let $ \sqrt{u} = t $, so $ u = t^2 $. Substituting into the equation:

📌 t^2 \cdot t - 6t^2 + 7t - 12 = 0 \Rightarrow t^3 - 6t^2 + 7t - 12 = 0

📌 We are now to find the sum of the roots of the cubic equation

📌 t^3 - 6t^2 + 7t - 12 = 0

📌 By **Vieta’s Formula**, the sum of the roots is the coefficient of $ t^2 $ with the opposite sign:

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