Question

Question #0e711

Answer 1

None of the choices are true. Perhaps `f(x)` should be `4x^(color(red)3)-x^2+10x-6`. If so, the answer is (D).

Explanation:

First, reduce the function.
`F(x)=3x^2+10x-6`.

In the rational root test, possible rational roots of F(x) are the form
`x=+-("divisor of "6)/("divisor of "3)`, or, `x=+-(1,2,3,6,1/3,2/3)`

So there are `12` possible rational roots.

However, none of them are the actual roots. The actual roots of `3x^2+10x-6=0` are `x=(-5+-sqrt(43))/3`.

If `f(x)=4x^(color(red)3)-x^2+10x-6`, possible rational roots are
`x=+-("divisor of "6)/("divisor of "4)`. They are `+-(1,2,3,6,1/2,3/2,1/4,1/3)`, and the answer is (D).

Again, none of the possible `16` rational roots pass the test.
The roots of `4x^3-x^2+10x-6=0` are irrational, and they are approximately `x=0.56088, -0.1554+-1.6279i`
(caluculated in http://www.wolframalpha.com/input/?i=4x%5E3-x%5E2%2B10x-6)