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Home » given that all roots are real and non-negative. - Simpleprint

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

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 Substitute \( p = 1 \), \( q = 1 \), \( r = 1 \) into equation (1):

📌 \[ 1 + 1 + 1 + s = 3 \Rightarrow s = 0 \]

📌 Thus, the coefficients are \( p = 1 \), \( q = 1 \), \( r = 1 \), \( s = 0 \).

📌 \(\boxed{p = 1, \, q = 1, \, r = 1, \, s = 0}\)

📌 A biologist is studying a population of beetles whose growth rate follows a cubic function \( f(x) = ax^3 + bx^2 + cx + d \). Observations show \( f(1) = 4 \), \( f(2) = 15 \), \( f(3) = 40 \), and \( f(4) = 85 \). Determine the coefficients \( a \), \( b \), \( c \), and \( d \).

📌 We solve the system from:

📌 \( a + b + c + d = 4 \)

📌 \( 8a + 4b + 2c + d = 15 \)

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