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Answer :
Answer:
The zeros of the function f(x) = 9x^3 - 45x^2 + 36x is 0, 1, 4
Solution:
Given that [tex]f(x)=9 x^{3}-45 x^{2}-36 x[/tex]
For finding the zeros of the function, we equate the entire function to zero i.e.,
[tex]0=9 x^{3}-45 x^{2}+36 x[/tex]
Dividing throughout by 9, we get
[tex]0=x^{3}-5 x^{2}+4 x[/tex]
Taking x as common throughout the equation, we get
[tex]0=x\left(x^{2}-5 x+4\right)[/tex]
Thus, by factorization of the above equation, we get 0 = x(x - 1)(x - 4)
Now ,equating the factors we got to 0, we get
x = 0, x - 1 = 0, x - 4 = 0
x = 0, x = 1, x = 4
Thus, the zeros of the above given function are 0, 1, 4
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