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Home » They Said It Was a Waste of Time—But Trying Try Changed Everything Forever! - Abbey Badges

They Said It Was a Waste of Time—But Trying Try Changed Everything Forever! - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Question:** A Martian subsurface spectroscopic engineer models the likelihood of mineral detection with the function \( m(x) = 2x^3 - 9x^2 + 12x - 4 \). Find the points where the likelihood is zero.

📌 Solution:** To determine where the likelihood is zero, solve \( m(x) = 2x^3 - 9x^2 + 12x - 4 = 0 \).

📌 First, apply the Rational Root Theorem to test possible rational roots, which are factors of the constant term \(-4\) over factors of the leading coefficient \(2\): \( \pm 1, \pm 2, \pm 4, \pm rac{1}{2}, \pm rac{1}{4} \).

📌 m(1) = 2(1)^3 - 9(1)^2 + 12(1) - 4 = 2 - 9 + 12 - 4 = 1

📌 m(2) = 2(2)^3 - 9(2)^2 + 12(2) - 4 = 16 - 36 + 24 - 4 = 0

📌 So, \( x = 2 \) is a root. Use synthetic division to divide \( m(x) \) by \( x - 2 \):

📌 & 2 & -9 & 12 & -4 \

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