SOLUTION: 2x^3-13x^2+24x-9=0 How do I find zeros?

Question 693647: 2x^3-13x^2+24x-9=0
How do I find zeros?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Any rational zeros would be of the form ,
with being a factor of the constant (),
and being a factor of the leading coefficient ()
Factors of are 1, 3, and 9.
Factors of are 1, and 2.
Possible rational zeros are -1/2, -3/2, -9/2, -1, -3, -9, 1/2, 3/2, 9/2, 1, 3, and 9.
Descartes rule of signs helps narrow down your choices.
has 3 changes of sign going from one coefficient to the next. That means that it has 3 or 1 positive zeros. (It could be two different zeros if one is a double zero).
has 0 changes of sign, meaning that there are 0 negative zeros.
Now we say that possible rational zeros are 1/2, 3/2, 9/2, 1, 3, and 9.
Trying the possible zeros, using synthetic division, we find out that

Then we recognize that and have the complete factorization,
,
which tells us that the zeros are (with multiplicity 2, a double zero), and

RELATED QUESTIONS
"Find the zeros of the polynomial equation X^4 + 2X^3 - 13X^2 - 14X + 24 =... (answered by MathLover1,greenestamps)

I don't get how to find the zeros or what the x=-3 is for. f(x)=x^4+2x^3-13x^2-38x-24... (answered by checkley75)

How do I factor completely... (answered by scott8148)

I need help finding the zeros of: F(x)=... (answered by MathLover1,stanbon)

I need to find all zeros. 13x(exponent 3)-185x(exponent... (answered by stanbon)

I need to find all zeros... (answered by KMST)

how do you find the zeros of the polynomial... (answered by Fombitz)

How do I simplify (15x^2-24x+9) divided by... (answered by jim_thompson5910)

How to find exact zeros of... (answered by Fombitz)