# How do you find all zeroes for #f(x)=2x^3-3x^2+1#?

##### 1 Answer

Feb 1, 2017

The zeros of

#### Explanation:

Given:

#f(x) = 2x^3-3x^2+1#

First note that the sum of the coefficients is

#2-3+1 = 0#

Hence

#2x^3-3x^2+1 = (x-1)(2x^2-x-1)#

Note that the sum of the coefficients of the remaining quadratic is also zero:

#2-1-1 = 0#

So

#2x^2-x-1 = (x-1)(2x+1)#

From the last linear factor we can see that the remaining zero is