Question

2x^4 - x^3 + 2x - 2 = 0. Show that the equation has a root in the given interval [-2,-1] .

Answer 1

imagine a general polynomial graphed out as follows:

if it crosses the x-axis somewhere along its path, then you know that the value of the function just before it crosses that point and its value just after it crosses that point must be of different signs.

i.e. the value of the function has to either go from a positive value to a negative value, or from a negative to a positive value.