Question

Find the zeros of the function.
f(x) = 9x^3 - 45x^2 + 36x

Answer 1

Answer:

x=0

x=1

x=4

Step-by-step explanation:

Answer 2

Answer:

The zeros of the function f(x) = 9x^3 - 45x^2 + 36x is 0, 1, 4

Solution:

Given that $f(x)=9 x^{3}-45 x^{2}-36 x$

For finding the zeros of the function, we equate the entire function to zero i.e.,

$0=9 x^{3}-45 x^{2}+36 x$

Dividing throughout by 9, we get

$0=x^{3}-5 x^{2}+4 x$

Taking x as common throughout the equation, we get  

$0=x\left(x^{2}-5 x+4\right)$

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