1. ## positive roots?

Hi can someone help.

Q. Determine whether these equations have positive roots

$\displaystyle i)\ s^3 + 6s^2 + 11s + 6 = 0$
$\displaystyle ii)\ s^3 + s^2 - 8s - 12 = 0$

Cheers

2. Originally Posted by anothernewbie
Hi can someone help.

Q. Determine whether these equations have positive roots

$\displaystyle i)\ s^3 + 6s^2 + 11s + 6 = 0$
$\displaystyle ii)\ s^3 + s^2 - 8s - 12 = 0$

Cheers
The first equation has a root at -2, so by synthetic division you can write the $\displaystyle (s+2)(-2s^2-8s-6)=0$ You know how to solve quadratics right? Find the roots of $\displaystyle -2s^2-8s-6=0$.

3. thanks, i get (-3,-1), I am still a little confused about how you found the first one to have a root of -2?

Cheers

4. 1) If s>0 then $\displaystyle s^3+6s^2+11s+6>0$. Then the equation has no positive real root.

2) $\displaystyle s=3$ is one of the roots.

Then $\displaystyle s^3+s^2-8s-12=(s-3)(s+2)^2=0$

The other two roots are equal with -2.

5. Originally Posted by anothernewbie
thanks, i get (-3,-1), I am still a little confused about how you found the first one to have a root of -2?

Cheers
I used calculus to guess the root. There's different ways you can find roots. If you find just one, you can find the others easily. There are a set of equations you can find here:

Vičte's formulas - Wikipedia, the free encyclopedia