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📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 A quadratic equation is given by \( ax^2 + bx + c = 0 \). If the roots are 3 and -5, find the equation given that \( a = 2 \).

📌 The sum of the roots is \( 3 + (-5) = -2 \).

📌 The product of the roots is \( 3 \times (-5) = -15 \).

📌 The equation in terms of roots is \( x^2 - (\text{sum of roots})x + (\text{product of roots}) = 0 \).

📌 Substituting gives \( x^2 + 2x - 15 = 0 \).

📌 Since \( a = 2 \), multiply the entire equation by 2: \( 2x^2 + 4x - 30 = 0 \).

📌 #### \( 2x^2 + 4x - 30 = 0 \)

📌 A circle is inscribed in a square. If the area of the square is 64 square units, what is the circumference of the circle?

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