# Solve a cubic

• Oct 7th 2011, 01:38 AM
Mhmh96
Solve a cubic
I need solve this equation

\$\displaystyle x^3+2x^2+2x+1=0\$
• Oct 7th 2011, 03:49 AM
Prove It
Re: Solve equation
Quote:

Originally Posted by Mhmh96
I also need solve this equation ^

Can you find a value of x that makes the LHS = 0?
• Oct 7th 2011, 05:57 AM
sbhatnagar
Re: Solve equation
The factors of \$\displaystyle x^3+2x^2+2x+1\$ are \$\displaystyle (1 + x) (1 + x + x^2)\$.

Now, roots of the equation can be found.
• Oct 8th 2011, 02:28 AM
sankalpmittal
Re: Solve equation
Quote:

Originally Posted by sbhatnagar
The factors of \$\displaystyle x^3+2x^2+2x+1\$ are \$\displaystyle (1 + x) (1 + x + x^2)\$.

Now, roots of the equation can be found.

Correct though.
@ Mhmh96

You can use factor theorem to factorize this equation : x^3+2x^2+2x+1
What are the factors of 1 ?
1 AND -1
-1 is satisfying the equation to 0
f(-1) =0
so
x+1 is factor of x^3+2x^2+2x+1
Now use division method .
Quotient will be
(1 + x + x^2)

So x^3+2x^2+2x+1 = (x+1)(1 + x + x^2)