Finding Roots for a Challenging Polynomial Equation

[thomasrules]

What are the ROots:

x^4+4x^3+14x^2=-4x-13

ok the 13 really causes a problem because you can't factor that.
So I move the right side to the left and then you can't find a number that fits so that it equals zero so I tried factoring it somehow but can't do it can someone help?

 

[Data]

That's a fairly evil problem to give you, but oh well (if I needed to solve it, I'd just throw it into maple and not think about it!).

It's written that way for a reason. Factor the left side and rearrange to change it to

$$x^2(x^2 + 4x + 14) + (4x + 13) = 0.$$

Do you see how to factor it now?

 

[thomasrules]

no lol

well i have to use the quadratic formula?

 

[Data]

Yes, and all the roots are complex. Are you sure you don't see how to factor that? I'll rewrite it this way:

$$x^2(x^2 + 4x + 13) + x^2 + (4x + 13) = 0$$

 

[thomasrules]

i thought u were trying to lead me to grouping them to factor but doesn't look like that...

NEVER MIND HOLD ON IM RETARDED

 

[thomasrules]

Hey Data take a look :

$$(x^2+1)(x^2+4x+13)$$

?

 

[Data]

looks good

 

[thomasrules]

<3 you :!)

 

[access_084]

in matlab:

>>p= x^4+4x^3+14x^2+4x+13;
>>roots(p)its very easy...heheh

 

[arildno]

Yes, relying on the previous work of intelligent people is always the easiest way.