What are the roots of the polynomial equation x^3-10x=-3x^2+24? use a graphing calculator and a system of equations. a. -24, -3, 12 b. -12, 3, 24 c. -4, -2, 3 d. -3, 2, 4

Answer : C

the roots of the polynomial equation x^3-10x=-3x^2+24

We use a graphing calculator

Graph the left hand side expression using graphing calculator

We graph

Then we graph the right hand side expression using graphing calculator

so we got two system of equations

The intersection of two graphs is our solution

The graph is attached below

We can see that the graph intersects at 3 points

(-4, -24)  (-2,12) and (3,-3)

So the roots are -4, -2 , 3

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the answer will be d: 2