Question #0e711

1 Answer
Dec 19, 2017

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)