the roots of the function is 0, 1 and 9 (option D)
see graph below
Explanation:
The given function:
[tex]f\mleft(x\mright)=x^3-10x^2+9x[/tex]
We need to find the root of the function. The roots are the value of x when f(x) = 0
[tex]\begin{gathered} 0=x^3-10x^2+9x \\ 0=x(x^2\text{ - 10x + 9)} \\ x\text{ = 0} \\ or\text{ }x^2\text{ - 10x + 9 = 0} \end{gathered}[/tex][tex]\begin{gathered} x^2\text{ - 10 x + 9 = 0} \\ x^2\text{ -9x - x + 9 = 0} \\ x(x\text{ - 9) -1(x - 9) = 0} \\ (x\text{ - 1)(x - 9) + 0} \\ x\text{ - 1 = 0 or x -9 = 0} \\ x\text{ = 1 or x = 9} \end{gathered}[/tex]
So, the roots of the function is 0, 1 and 9
These are the points the line crosses the x axis.
We need to check for the graph whose line crosses he x axis at x = 0, x = 1 and x = 9 (option D)
