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

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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 :

$x^{3} - 1 = (x - 1) (x^{2} + x + 1)$ $x^3 - 1 = (x-1)(x^2 + x + 1)$

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:

$x = \frac{- 1 \pm \sqrt{1 - (4) (1) (1)}}{(2) (1)}$ $x = [-1 +- sqrt(1 - (4)(1)(1))] / [(2)(1)]$

$x = - 0.5 \pm 0.5 i \sqrt{3}$ $x = -0.5 +- 0.5isqrt(3)$

Hope that helped!

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