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

Let's solve your equation step-by-step.

x3 - 10x = - 3 x2 + 24

Step 1: Subtract - 3x^2+24 from both sides.

x3 - 10x - ( - 3 x2 + 24) = - 3 x2 + 24 - ( - 3 x2 + 24)

x3 + 3 x2 - 10x - 24 = 0

Step 2: Factor left side of equation.

(x+2) (x-3) (x+4) = 0

Step 3: Set factors equal to 0.

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

x = - 2 or x = 3 or x = - 4

Answer:

x = - 2 or x = 3 or x = - 4