Question

Is 1/3 a zero of f(x) = 2x^3 + 3x^2 - 6x + 7 ? Explain.

Answer 1

\[f(x)=2x^3+3x^2-6x+7\]
if 1/3 is a zero then put x=1/3 in f(x)
\[f(1/3) =0\]
Can you check this?

Answer 2

a simpler way is to check to see if its a part of the possible rational roots

Answer 3

\[\pm\frac{factors.of.last}{factors.of.first}\]

Answer 4

I replaced x with 1/3, and my answer was 5.407. So 1/3 is not a zero of the polynomial because when x is replaced by 1/3, the sum is not 0. correct?

Answer 5

thats a suitable check, so yes

Answer 6

thank you

Answer 7

the rational roots test would have told us that we need a 1 or a 2 in the denominator to have a chance of being a root to begin with;

since 3 is not a 1 or a 2, it has no chance of being a root