SOLUTION: Can you please help me with this problem? I have no idea how to find any of the zeros!!! Find a rational zero of the polynomial function f(x)=3x^3

SOLUTION: Can you please help me with this problem? I have no idea how to find any of the zeros!!! Find a rational zero of the polynomial function f(x)=3x^3 - 17x^2 + 18x +8, then use it

Question 45236: Can you please help me with this problem? I have no idea how to find any of the zeros!!!
Find a rational zero of the polynomial function f(x)=3x^3 - 17x^2 + 18x +8, then use it to find all the zeros of the function.

Thank You!!

Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
Do you have a graphing calculator? If so, then you can graph the function, and see where it crosses the x axis. These would be zeros of the rational function (actually it is a polynomial function!)

From the graph above, you can see that there are zeros at x = 2 and x=4, with a third root at x=-1/3. Since the polynomial is of degree 3, there are only three roots, so this must be the three roots: x = -1/3, 2, and 4.

You can verify these roots by synthetic division by either 2 or 4 (or -1/3 I suppose!), which will give you a reduced equation that is quadratic. This quadratic equation can be solved by factoring.

NOTE: This is NOT the traditional way to solve this problem. The great French mathematician Rene Descartes is either VERY PROUD of us, or he is turning over in his grave!!

R^2 at SCC

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