SOLUTION: Find all the rational zeros of f(x) = 6x^3–3x+11x^2–2.

Algebra ->  Rational-functions -> SOLUTION: Find all the rational zeros of f(x) = 6x^3–3x+11x^2–2.       Log On


   

Question 324761: Find all the rational zeros of f(x) = 6x^3–3x+11x^2–2.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
+graph%28+300%2C+300%2C+-3%2C+3%2C+-10%2C+10%2C++6x%5E3-3x%2B11x%5E2-2%29
Looks like highlight%28x=-2%29 is a zero, verify using the equation.
6%28-8%29-3%28-2%29%2B11%284%29-2=-48%2B6%2B44-2=0
You can guess the other two or you can use polynomial long division to get the remaining quadratic equation.
%286x%5E3-3x%2B11x%5E2-2%29%2F%28x%2B2%29=6x%5E2-x-1
You can then factor this quadratic,
6x%5E2-x-1=%283x%2B1%29%282x-1%29
Which yields,
3x%2B1=0
3x=-1
highlight%28x=-1%2F3%29
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2x-1=0
2x=1
highlight%28x=1%2F2%29