x^3-3x^2+2=0?

Answer 1

By inspection, x=1 is a zero of the equation. That means x-1 is a factor. You can either use long division with x-1 or synthetic division with 1 to find the other quadratic factor of x² -2x - 2. Find that factor's zeros and you will have all the zeros of the cubic. Hence, x=1, 1±sqrt3

Answer 2

x^3 - 3x^2 + 2 = 0

The first thing to do is find out if the function has any integral
factors. Because the constant is 2, the only factors that need
assessing are (x - 1), (x + 1), (x - 2) and (x + 2), in other
words, is x equal to 1, -1, 2 or -2, respectively.

Beginning with x = 1, we have 1^3 - 3*1^2 + 2 = 0, so the
function is true for x = 1. Thus we know that (x - 1) is a factor.

Now divide (x - 1) into x^3 - 3x^2 + 2 by synthetic division.
The result is x^2 - 2x - 2.

This is a quadratic and it doesn't appear to have any
integral factors, so use the quadratic formula to find x.

x^2 - 2x - 2 = 0 implies that

x = {-(-2) ± sqrt[(-2)^2 - 4(1)(-2)]} / (2*1)

= [2 ± sqrt(12)] / 2

= [2 ± 2*sqrt(3)] / 2

= 1 ± sqrt(3)

Therefore, x^3 - 3x^2 + 2 = 0 has the solutions :

x = 1, or x = 1 - sqrt(3), or x = 1 + sqrt(3).

Answer 3

x^3-3x^2+2=0

I can see at a glance that x=1 is a solution so

                  x^2 - 2x -2
x-1⌐x^3 - 3x^2 + 0x + 2
     -(x^3 - x^2)
               -2x^2 + 0x
              -(-2x^2 + 2x)
                            - 2x + 2
     -(-2x + 2)
        0
x^3-3x^2+2=(x-1)(x^2-2x-2)=0
x-1=0
x=1
x^2-2x-2=0

x=(2±√(4+8))/2
x=(2±√12)/2
x=1±2√3
x=1, 1+2√3, 1-2√3

Answer 4

x^3-3x^2+2=0

(x-1) (x^2 + 2x -2) =0

This implies that x=1 or x = {-2 +/- [4 - 4(-2)]^0.5 } / 2

Hence, x =1, or x= -1 + 3^0.5, or x = -1 - 3^0.5

Answer 5

x^3-3x^2+2=0
=(x-1)(x^2-2x-2)
x-1= 0 --> x = 1
x= [2+/- sqrt(4+8)]/2
x = 1 +/- sqrt(3)
So x = 1, 1+sqrt(3) and 1-sqrt(3)

Answer 6

x^3-3x^2+2=0
x^3-x^2 -2x^2+2=0
x^2(x-1)-2(x-1)(x+1)=0
(x-1)(x^2-2x-2)=0

x1=1
x2=1+sqrt 3
x3=1-sqrt 3

Answer 7

o=2=2^x3-3^x

Answer 8

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

Answer 9

X=-0.732, 1, 2.732

Answer 10

o gosh.