# How do you find the zeroes for #3x^4 - 4x^3 + 4x^2 - 4x + 1#?

##### 2 Answers

The zeros are

#### Explanation:

The Rational Roots Theorem implies that if

If you check

Doing long division (or synthetic division) leads to

Use the rational zeros theorem (or the sum of the coefficients "shortcut") to find that

#### Explanation:

So,

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

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

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

The real zeros are