According to the roots of the polynomial, it is found that the correct statement is given by:
- The graph crosses the x axis at x = 0 and touches the x axis at x = 3.
What are the roots of a function?
- The roots of a function are the values of x for which f(x) = 0.
In this problem, the function is:
[tex]f(x) = x^5 - 6x^4 + 9x^3[/tex]
Factoring it, we have:
[tex]f(x) = x^3(x^2 - 6x + 9) = x^3(x - 3)^2[/tex]
Hence:
- It crosses the x-axis at x = 0, as it is a root of multiplicity 3, which is an odd number.
- It touches the x-axis at x = 3, s it is a root of multiplicity 2, which is an even number.
You can learn more about the roots of a polynomial at https://brainly.com/question/24380382
