Arlana graphed the system of equations that can be used to solve x^3-5x^2+2=-x^3+17x. What are the roots of the polynomial equation? Round noninteger roots to the nearest hundredth.

Using a graphing program (see attached picture), the roots are -2, .11, and 4.39.

Note: it took some time to figure out a window that would show both graphs well enough to see the three intersections.

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xero099 xero099 · Answer 2 · 2021-11-23T14:33:26+01:00

The roots of the resulting polynomial equation are [tex](x_{1},y_{1}) = (-2,-26)[/tex], [tex](x_{2}, y_{2}) = (0.11,1.94)[/tex] and [tex](x_{3},y_{3}) = (4.39,-9.81)[/tex], respectively.

Ariana must graph two polynomic expressions: [tex]f(x) = x^{3}-5\cdot x^{2}+2[/tex] and [tex]g(x) = -x^{3}+17\cdot x[/tex]. The roots of the resulting polynomial equation are found by means of this formula:

[tex]f(x) - g(x) = 0[/tex] (1)

Then, we must look for every point so that [tex]f(x) = g(x)[/tex].

The roots of the resulting polynomial equation are [tex](x_{1},y_{1}) = (-2,-26)[/tex], [tex](x_{2}, y_{2}) = (0.114,1.937)[/tex] and [tex](x_{3},y_{3}) = (4.386,-9.812)[/tex], respectively.

We kindly invite to check this question on polynomials: https://brainly.com/question/23792383