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

Question

6085 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-09-23T18:41:56

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

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!

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