0=9x^3+6x^2+x

Question

i didn't get an answer to this problem , i think I did the steps wrong

Answer 1

9x^3 + 6x^2 + x = 0

 

Factor it as much as you can:

 

9x^3 + 6x^2 + x = x(9x^2 + 6x + 1)

 

x=0 is one solution; use the quadratic formula to find two more:

 

x = {-6 ± √[(6)^2 - 4(9)(1)]} / (2*9) = (1/18)(-6 ± 0) = -1/3

 

So the solutions are x=0 with a multiplicity of 1, and x = -1/3 with a multiplicity of 2

Answer 2

0= 9x³ + 6x² + x

 

First, you'll want to factor out an x:

 

0= x (9x² + 6x + 1)

 

Now, factor a little more!

 

0= x (3x + 1)(3x + 1) or 0= x (3x + 1)²

 

You will have two solutions:

 

x = 0 and (3x + 1)² = 0

 

3x + 1 = 0

3x = -1

x = -1/3

 

x = -1/3, 0