SOLUTION: Find a rational zero of the polynomial function and use it to find all the zeros of the function. f(x) = 2x^3 - x^2 - 12x + 6

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Find a rational zero of the polynomial function and use it to find all the zeros of the function. f(x) = 2x^3 - x^2 - 12x + 6      Log On


   

Question 166450: Find a rational zero of the polynomial function and use it to find all the zeros of the function. f(x) = 2x^3 - x^2 - 12x + 6
Answer by stanbon(75887) About Me  (Show Source):
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Find a rational zero of the polynomial function and use it to find all the zeros of the function. f(x) = 2x^3 - x^2 - 12x + 6
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I graphed it and found that x= 0.5 is a zero.
Use synthetic division to find the other zeroes:
0.5).....2....-1....-12....6
........2.....0.....-12..|..0
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Quotient: 2x^2-12
Remainder: 0
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Find the zeroes of the quotient:
2x^2-12 = 0
x^2 = 6
x = sqrt(6) or x = -sqrt(6)
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The zeroes are x = 0.5, or sqrt(6) or -sqrt(6)
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Cheers,
Stan H.