How do I use a graphing calculator to find the complex zeros of x^3-1x31?

1 Answer
Sep 23, 2015

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)x31=(x1)(x2+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=1±1(4)(1)(1)(2)(1)

x = -0.5 +- 0.5isqrt(3)x=0.5±0.5i3

Hope that helped!