Answer:
Hence, the roots of the polynomial equation are:
-2, 1, 4
Step-by-step explanation:
We are asked to find the roots of the polynomial equation:
[tex]x^3-6x=3x^2-8[/tex]
We can also equate this equation to y to obtain a system of equation as:
[tex]y=x^3-6x[/tex]
and [tex]y=3x^2-8[/tex]
Hence, the roots of the polynomial; equation are the x-values of the point of intersections of the graph of the system of equations.
Hence, the point of intersection of the two graphs are:
(-2,4), (1,-5) and (4,40)
Hence, the roots of the polynomial equation are:
-2, 1, 4
