Question

Find the zeros of the function. f(x) = 3x3 - 21x2 + 36x

Answer 1

3x(x^2 -7x +12) = 3x(x-4)(x-3)

3x=0
x_1 = 0

x-4=0
x_2 = 4

x-3=0
x_3 = 3

hope helped 

Answer 2

Answer:  The required zeroes of the given function are 0, 3 and 4.

Step-by-step explanation:  We are given to find the zeroes of the following function :

$f(x)=3x^3-21x^2+36x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We know that the zeroes of the function y = f(x) are given by f(x) = 0.

Therefore, from equation (i), we get

$f(x)=0\\\\\Rightarrow 3x^3-21x^2+36x=0\\\\\Rightrarow 3x(x^2-7x+12)=0\\\\\Rightarrow 3x=0,~~x^2-7x+12=0\\\\\Rightarrow x=0,~~\Rightarrow x^2-3x-4x+12=0\\\\\Rightarrow x=0,~~\Rightarrow x(x-3)-4(x-3)=0\\\\\Rightarrow x=0,~~\Rightarrow (x-3)(x-4)=0\\\\\Rightarrow x=0,~~x-3=0,~~x-4=0\\\\\Rightarrow x=0,3,4.$

Thus, the required zeroes of the given function are 0, 3 and 4.