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Finding the zeroes of an equation means finding the x-values for which the function is equal to 0.
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Let us set the function's value to 0 and rewrite the equation.
0 = x³ - 9x² + 23x - 15
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Finding divisors of our constant term
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1, 3, 5, 15
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Brute Force
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0 = 1 - 9 + 23 - 15 YEP
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(x - 1) can be factored out
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0 = (1)³ - 9(1)² + 23(1) - 15
(x³ - 9x² + 23x - 15) / (x - 1)
Ruffini's method
(x² - 8x + 15)(x - 1)
x² - 8x + 15 = 0
(x - 5)(x - 3) = 0
ZEROES
x = 1
x = 5
x = 3
(x - 5)(x - 3)(x - 1)
x - 1 = 0
x - 5 = 0
x - 3 = 0
prompt was x=1
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