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when is stranger things volume 2 coming - Parker Core Knowledge

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 5**Question:

📌 Compute the sum of the roots of the equation \( v\sqrt{v} - 4v + 5\sqrt{v} - 6 = 0 \) given that all of the roots are positive.

📌 Let's transform the given equation using a substitution. Let \( x = \sqrt{v} \). Then \( v = x^2 \). Substitute into the equation:

📌 x^2 \cdot x - 4x^2 + 5x - 6 = 0

📌 which simplifies to:

📌 x^3 - 4x^2 + 5x - 6 = 0

📌 Now, we need to find the sum of the roots of this cubic equation. In a cubic equation of the form \( ax^3 + bx^2 + cx + d = 0 \), the sum of the roots is given by:

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\[ 5h + 6h - 12 = 15 \]
\[ 11h - 12 = 15 \]
Add 12 to both sides:
\[ 11h = 27 \]
Divide by 11:
\[ h = \frac{27}{11} \]
Now substitute \( h = \frac{27}{11} \) back into \( k = 2h - 4 \):
\[ k = 2\left(\frac{27}{11}\right) - 4 \]
\[ k = \frac{54}{11} - \frac{44}{11} \]
\[ k = \frac{10}{11} \]

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