Question

Show that the equation x3+6x-5=0 has a solution between x=0 and x=1

Answer 1

see explanation

Explanation:

substitute x = 0 and x = 1 into the polynomial and evaluate

0³ + 6(0) - 5 = 0 + 0 - 5 = - 5

1³ + 6(1) - 5 = 1 + 6 - 5 = 2

since polynomial < 0 at x = 0 and > 0 at x = 1

Then the graph crosses the x- axis between 0 and 1

This indicates the solution lies between x = 0 and x = 1