Answer:
x ∈ {0, -1 -√6, -1 +√6}
Explanation:
You want to use a graphing calculator to find the roots of ...
f(x) = x³ +2x² -x
Calculator
There are many ways to solve this using a graphing calculator. The first two attachments show the use of a Solver function. The solution is shown first. The second attachment shows the Solver setup.
The roots are ...
x ∈ {0, -1 -√6, -1 +√6}
Graph
The third attachment shows a graph of the function (green). Its one rational root is x = 0. Dividing the function by the factor (x -0) reveals the quadratic factor (g(x), red). Quadratics are often easily solved from their graph by noting the coordinates of the vertex, (-1, -6).
When the quadratic is written in vertex form with a leading coefficient of 1, the roots are easily found:
g(x) = (x -h)² +k ⇒ x = h ±√(-k)
Here, the irrational roots are ...
g(x) = (x +1)² -6 ⇒ x = -1 ±√6
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