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Finding the zeroes of an equation means finding the x-values for which the function, in this case f(x), is equal to 0.
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Let us set the function's value to 0 and rewrite the equation.
0 = 6x³ - 7x² - 9x - 2
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Finding the divisors for the constant
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1, 2
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Brute Force
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0 = 6 - 7 - 9 - 2 NOPE
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0 = 48 - 28 - 18 - 2 YEP
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So we know now that (x - 2) can be factored out
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Using Ruffini's
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(6x³ - 7x² - 9x - 2) / (x - 2)
0 = 6(1)³ - 7(1)² - 9(1) - 2
0 = 6(2)³ - 7(2)² - 9(2) - 2
Ruffini's method
6x² + 5x + 1 = 0
(3x + 1)(2x + 1) = 0
WAIT HOW DID YOU GET THIS
Trial&Error / Plug&Play / Brute Force
(3x + 1)(2x + 1)(x - 2)
3x + 1 = 0
2x+ 1 = 0
x - 2 = 0
ZEROES
x = -(1/3)
x = -(1/2)
x = 2
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