Question

List all the possible rational zeros of
p(x)=2x^3-3x^2+4x-6.

Answer 1

p(x)=2x^3-3x^2+4x-6
y=x^2(2x-3)+2(2x-3)
y=(2x-3)(x^2+2)
now set it to zero and solve for each of the brackets (idk if we can do this, since it already =y but i can't think of anything else to do...)
0=(2x-3)(x^2+2)
0=2x-3
2x=3
x=3/2 and now the 2nd eqt
0=x^2+2
-2=x^2
root of -2=x (unless you're working with i, this is impossible so we eliminate this answer)
so we are left with x=3/2

Answer 2

You are not being asked to find one actual zero / root / solution of this problem, and there's no equation here, only the definition of a function: p(x)=2x^3-3x^2+4x-6.

Please refer to this web page:

http://www.virtualnerd.com/algebra-2/polynomials/roots-zeros/rational-zero-theorem/rational-zeros-example

and make certain you understand what "rational zeros" are, before trying to solve this problem.

Answer 3

Okay :)

Answer 4

Possible rational zeros are identified as follows:
List all possible factors of the constant term of your polynomial. In this case that constant term is -6. As an example, I'm typing out for you the factors of -6:\[\pm1,\pm2,\pm3,\pm6\]

Answer 5

Now do the same thing for the coefficient of your highest-order term. In this problem that coefficient is 2. What are all the possible factors of 2?