Question

HELP ME. IT'S EASIER THAN YOU THINK

determine between which consecutive integers the real zeros of the function are located: x^3-2x^2+5x-3 (and approximate the real zeros above to the nearest tenth)

Answer 1

Let f(x) = x^3 - 2x^2 + 5x - 3
Try successive integer values for x until f(x) changes sign (either from a positive to a negative value or from a negative to a positive value). As soon as you find two integers that changes the sign of f(x) we know there must be a point in between those two x values that makes f(x) equal zero.
f(0) = -3
f(1) = 1 - 2 + 5 - 3 = +1
f(x) changes sign between x = 0 and x = 1. Therefore, there must be an x value in between that makes f(x) = 0.
Now try x = 0.5
f(0.5) = ?
Does f(x) change sign between x = 0 and x = 0.5 OR between x = 0.5 and x = 1
Then take the midpoint of that interval and find f(x). Keep repeating this process until the first decimal place does not change.