f(x) = 6x^3-7x^2+1

Question

Considering the Function:

List all possible rational zeros: ___, ___, ____, ___, ____,____

Find one rational zero using Synthetic Division. x=____

Solve completely over the real numbers.  List all zeros.

x= ___, ___, ___

Answer 1

f(x) = 6x^3-7x^2+1

f(x) = 6x^3-7x^2+0x+1

the first term is x+1 or x-1

     ______________

x-1)6x^3-7x^2+0x+1

1 |  6   -7  0  1

   |____6_-1-1___

      6   -1 -1 0

So the first term is (x-1) and 6x^2-x-1

Using rainbow method

6x^2-x-1, a=6, b = -1, c=-1

Rewrite drop a and multiply c by a

x^2 – x – 6  factor

(x - 3)(x + 2)now divide the numbers by 6

(x-3/6)(x +2/6)

(x – ½)(x+1/3)  since they are not whole numbers move the denominators up

(2x - 1) (3x + 1)

The three terms are (x-1) (2x-1) (3x+1) set to 0

x =1, x=1/2, x=-1/3