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9x^3 - 18x^2 + 10x = 0 factor completely, and solve for each polynomial [include all roots, real and complex numbers]
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Sep 22, 2022
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9x^3 - 18x^2 + 10x = 0
factor completely, and solve for each polynomial
[include all roots, real and complex numbers]
Mathematics
high-school
AmitA
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AmitA
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Answer:
{0, 1 + i/3, 1 - i/3}
Explanation:
9x³ - 18x² + 10x = 0
x(9x² - 18x + 10) = 0
x[9x² - 18x + 9 + 1) = 0
x[(3x - 3)² + 1] = 0
1. x = 0,
2. (3x - 3)² = - 1 ⇒ 3x - 3 = ± i ⇒ 3x = 3 ± i ⇒ x = 1 ± i/3
Northys
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Sep 27, 2022
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Northys
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