Identify the number of solutions or zeros of: f(x)=5x^(3)-6x^(2)+2x-3

I cant figure out this algebra 2 problem.. thanks for your help
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By substituting x=1 and 2 in the function we get the values -2 and 17, so there must be a solution in this range of x. Using trial and error and a calculator to home in on the solution I found that x=1.26035 approx. this appears to be the only solution.

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