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Home » -\frac1086 + d = 3 \implies -18 + d = 3 \implies d = 21 - Nelissen Grade advocaten

-\frac1086 + d = 3 \implies -18 + d = 3 \implies d = 21 - Nelissen Grade advocaten

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 An archaeologist studying ancient Egyptian civilization found a papyrus with a peculiar quadratic equation inscribed:

📌 \[ x^2 + bx + c = 0 \]

📌 The sum of the roots is equal to the negative of the coefficient of \( x \), which is \(-b\), and the product of the roots is \( c \). If the roots are in the ratio 3:2, find the values of \( b \) and \( c \).

📌 Let the roots be \( 3k \) and \( 2k \). By Vieta's formulas, the sum of the roots is:

📌 \[ 3k + 2k = 5k = -b \]

📌 \[ b = -5k \]

📌 \[ (3k)(2k) = 6k^2 = c \]

📌 We need values for \( b \) and \( c \) in terms of \( k \). To find \( k \), note that the roots are real numbers, and any \( k \) will satisfy the conditions provided \( b \) and \( c \) are expressed as above. However, for simplicity, we can express them in terms of \( b \) and \( c \):

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