Solving nonlinear equations for both real and imaginary problems

Question

Three examples 

 

X^3+5x^2=0

 

2x^4-x^3-6x^2=0

 

9x^4-28x^2+3=0

 

Answer 1

X³ + 5x² = 0

 

     x²(x+5) = 0

 

     x = 0 and -5

 

2x⁴ - x³ - 6x² = 0

 

     x²(2x² - x - 6) = 0

     x²(2x² - 4x + 3x - 6)

     x²(2x(x-2) + 3(x-2))

     x²(2x+3)(x-2) = 0

 

     x = 0, -3/2, 2

 

9x⁴ - 28x² + 3

 

     This one has already been answered on the Answers page

Answer 2

For the last one

 

 

9x⁴ - 28x² + 3 = 0

 

(9x² - 1)(x² - 3) = 0

 

 

Set the factors equal to zero.

 

9x² - 1 = 0                 and              x² - 3 = 0

 

9x² = 1                       and             x² = 3

 

x = ±√(1 / 9)              and              x = ±√3

 

 

x = -1 / 3                                        x = -√3

x = 1 / 3                                         x = √3

 

 

Because this equation has a degree of 4, we have 4 solutions.