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Home » This LEGO Death Star Changed CGI Forever—See What Makes It Suspiciously Real! - Silent Sales Machine

This LEGO Death Star Changed CGI Forever—See What Makes It Suspiciously Real! - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 A quadratic equation \( ax^2 + bx + c = 0 \) has roots 3 and -2. If \( a = 1 \), find \( b \) and \( c \), and determine the value of the expression \( b^2 - 4ac \).

📌 Using Vieta's formulas:

📌 Sum of roots \( = -rac{b}{a} = 3 + (-2) = 1 \).

📌 Product of roots \( = rac{c}{a} = 3 imes (-2) = -6 \).

📌 Therefore, \( b = -1 \) and \( c = -6 \).

📌 The expression is \( b^2 - 4ac = (-1)^2 - 4(1)(-6) = 1 + 24 = 25 \).

📌 \( S_{n-1} = 3(n-1)^2 + 5(n-1) = 3(n^2 - 2n + 1) + 5n - 5 = 3n^2 - 6n + 3 + 5n - 5 \)

📌 \( a_n = S_n - S_{n-1} = (3n^2 + 5n) - (3n^2 - n - 2) = 6n + 2 \)

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