Solve the equation 200x4 400x3 600x2 x smallest value x

Solve the equation. 200x^4 = -400x^3 + 600x^2 x = _____ (smallest value) x = _____ x = _____ (largest value)

Solution

200x⁴ = -400x³ + 600x²

200x⁴ + 400x³ - 600x² =0

200x² ( x² + 2x -3) =0

200x²{x² + 3x -x -3} =0

200x²{x(x+3) -1(x+3)} =0

200x²(x-1)(x+3) =0

x=0, x=1(largest), x=-3 (smallest)