SOLUTION: find a rational zero of the polynomial function and use it to find all the zeros of the function f(x)=x^3-6x^2+7x+2

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Question 526112: find a rational zero of the polynomial function and use it to find all the zeros of the function f(x)=x^3-6x^2+7x+2
Answer by lwsshak3(11628) 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)=x^3-6x^2+7x+2
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Using the rational roots theorem:
...0..|...1......-6........7..........2..............
...1..|...1......-5........2..........4............
...2..|...1......-4.......-1.........0 (2 is a root)
(x-2)(x^2-4x-1)
solve (x^2-4x-1) by following quadratic equation:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
answers are:
x=-0.236
or
x=4.236
..
Rational roots are: -0.236, 2, and 4.236