Answer:[tex]1,\frac{-1+\sqrt{33} }{2} ,\frac{-1-\sqrt{33} }{2}[/tex]
Step-by-step explanation:
Zeros of a equation are the solutions to the equation when its value becomes zero.
Given [tex]m^{3}-9m+8=0[/tex]
This is a cubic equation,so first guess a root.
Try trail and error with common roots like [tex]1,0,-1,2...[/tex]
The given equation is satisfied when [tex]1[/tex] is tried.
So,[tex]1[/tex] is a root of the given equation.
[tex]m-1[/tex] is factor of the equation.
Divide the given equation with the obtained factor to get a quadratic equation.
[tex]\frac{m^{3}-9m+8}{m-1}=m^{2}+m-8[/tex]
The roots of the above quadratic equation can be obtained by the formula
[tex]\frac{-b+\sqrt{b^{2}-4ac}}{2a}[/tex], [tex]\frac{-b-\sqrt{b^{2}-4ac}}{2a}[/tex]
Substituting gives,
[tex]\frac{-1+\sqrt{33} }{2} ,\frac{-1-\sqrt{33} }{2}[/tex]
