How do I use a graphing calculator to find the complex zeros of #x^3-1#?

1 Answer
Sep 23, 2015

Answer:

Graphing calculators can help you find real zeros but will not help you with complex roots.

Explanation:

Using the difference formula for perfect cubes :

#x^3 - 1 = (x-1)(x^2 + x + 1)#

So, this cubic has one real zero at x = 1. The other two roots are imaginary. You can use the quadratic formula to solve for these other two roots:

#x = [-1 +- sqrt(1 - (4)(1)(1))] / [(2)(1)]#

#x = -0.5 +- 0.5isqrt(3)#

Hope that helped!