## Cj1213 3 years ago Find x. 4x^3 - 6x^2 +1 =0

1. freewilly922

Do you know how to do synthetic division?

2. satellite73

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

3. freewilly922

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

4. satellite73

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

5. satellite73

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

6. satellite73

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

7. Cj1213

are you dividing to get this like synthetic division.

8. Cj1213

I need help with the steps getting started

9. freewilly922

|dw:1353292321982:dw| 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.

10. Cj1213

okay i'll figure it out it is a start.

11. freewilly922

Definitely write down what @satellite73 wrote down about how to choose what to check.

12. Cj1213

Its been awhile since ive worked with synthetic division. all the answers are not rational. but once I get 1/2 I can take the equation and do the quadratic formula to get the other answers