f(x) = x^3 + 2x - 6

Question

Fiind the upper and lower bounds within which all of the real zeros of the polynomial functions must lie

Answer 1

Looks like this problem wants you to find bounds (between which x-values) you can find "all possible" zeros. Two simple steps

 

1. Use the rational root test to find possible zeros.

 

Possible zeros: x = +/-1, +/-2, +/-3, +/-6

 

2. Determine from the possible zeros which two x-values are the highest positive and highest negative value. All possible zeros will fall within this "domain" of x-values. In this case, -6 and +6 are the most negative and most positive values, so the upper and lower bounds are (answer expressed in interval notation):

 

[-6, 6]

 

The brackets are closed because -6 and 6 could possibly be zeros to the function.

 

Hope this was insightful :)

Alex