helpp mee with algebra 2

Question

marshall claims that there is only one real zero in the function f(x)=4x³+7x²-5x+3 based on the table provided determine weather you agree with marshall. then name the intervals in which the zeros are located

X f(x)

--------------------

-3 -27

-2 9

-1 11

0 3

1 9

2 53

Answer 1

I would find your answer reasonable based on the table, but I am not 100% certain. Whenever you see a change in sign in f(x) between two x values, this indicates that the function must cross the x axis. Since f(-3)=-27 & f(-2)=9, the function must be zero between x=-3 & x=-2.

The reason that I am uncertain that based on the table this is the only zero is the course-ness of the x values listed. What if there are negative values of f between -1 & 0 or between 0 & 1. To be certain, rather than use integer values for x, place the equation in a spreadsheet and change values of x in 0.1 units instead of 1 unit [here x=-3,-2,-1,0,1,2].