So $ f(0) = d = \boxed{27} $

February 22, 2026

$So $ f(0) = d = \boxed{27} $$

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7(-\frac{5}{3}) + 3(15) + c = -4 \Rightarrow -\frac{35}{3} + 45 + c = -4 \Rightarrow c = -4 + \frac{35}{3} - 45 = -\frac{112}{3}
Now use $ a + b + c + d = 3 $:
-\frac{5}{3} + 15 - \frac{112}{3} + d = 3 \Rightarrow \left( -\frac{117}{3} + 15 \right) + d = 3 \Rightarrow -39 + 15 + d = 3 \Rightarrow d = 27
Question: A computational biologist is analyzing a genetic model where the number of possible gene expression patterns corresponds to the product of the roots of the equation
x\sqrt{x} - 7x + 10\sqrt{x} = 0.
Find this product.

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