Question

Use your graphing calculator to solve the equation graphically for all real solutions

x^3-4x+2x+4=0

Solutions:
x =


Make sure your answers are accurate to at least two decimals

Answer 1

x = -0.732, 2.00, 2.732

Explanation:

You want to solve x³ -4x² +2x +4 = 0 using a graphing calculator.

Graph

The solutions are the x-intercepts highlighted in the attached graph.

x = -0.732, 2.000, 2.732

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Additional comment

The integer solution x=2 tells us the equation can be factored as ...

(x -2)(x² -2x -2) = 0

The quadratic solution is x = 1±√3, which is what we suspect by looking at the numbers from the graphing calculator. (√3 ≈ 1.732)

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