Question

determining the number of roots of the equation 8x^3+12x^2-50x+135=0 and find also the interval(s) that isolate the roots.Are the roots isolated?

Answer 1

• one negative real root in [-5, -4]; two complex roots
• the complex roots cannot be isolated in the same way.

Explanation:

A graphing calculator is a wonderful tool for this. It shows the one real root to be near -4.062, so between -5 and -4.

The value of the cubic at x = -5 is -315; at -4 it is +15, so the root is definitely between those values.

The one real root is isolated to being between (-5, -315) and (-4, 15). The complex roots are not isolated.