Question

Find x. 4x^3 - 6x^2 +1 =0

Answer 1

Do you know how to do synthetic division?

Answer 2

1 and -1 do not work (check those first)
next possibility is \(\frac{1}{2}\) check that next

Answer 3

Where does the 1/2 guess come from? just standard practice for +1 endings?

Answer 4

the constant is 1
the leading coefficient is 4
possible rational zeros are fractions where the numerator divides 1 and the denominator divides 4

Answer 5

possible rational zeros are
\[\pm 1,\pm\frac{1}{2},\pm\frac{1}{4}\]

Answer 6

1 and -1 are easiest to check because you can pretty much do it in your head
after you see they don't work, i would try \(\frac{1}{2}\) and lo and behold it does work

Answer 7

are you dividing to get this like synthetic division.

Answer 8

I need help with the steps getting started

Answer 9

The biggest problem is that synth. Division is hard to show how to do on open study.
This is an example if you were to check if (x-1) divides 4x^3 - 6x^2 +1
with 4 -6 0 1 as the coefficients. You basically have 1| 4 -6 0 1
where the first 1 is a from (x-a) or (x-1) which is what we are checking.
so you drop the first number down 4 multiply it by 1 to get 4. Add this 4 to -6 to get -2. Multiply this again by 1 to get -2 to add this to 0 to drop a -2. Multiply this again by 1 to get -2 to add to the last 1 to get -1. Since this is not a 0 then (x-1) doesn't divide 4x^3 - 6x^2 +1. need to try again.