Determine the zeros of the polynomial function: f(x) = 3x^5 - 2x^4 + x^3 - 16x^2 + 3x - 8.

Question

Please show steps/work.

Answer 1

Note that the problem does not say rational zeroes. I may have entered wrongly, but I saw a solution near 1.949158859 and only one real solution - from the alternating nature of the signs, we know all solutions will be positive; the odd power guarantees at least one solution; the relatively small linear and cubic coefficients guide us toward there being only one solution. Note the plot from 0 to 2