For example if I had something like $\displaystyle (\lambda)(\lambda^2-1)-(\lambda-1)+(1-\lambda)$ how would I find the roots? Is there away to quickly factor it or an equation similar to the quadratic equation?
For example if I had something like $\displaystyle (\lambda)(\lambda^2-1)-(\lambda-1)+(1-\lambda)$ how would I find the roots? Is there away to quickly factor it or an equation similar to the quadratic equation?
$\displaystyle (\lambda)(\lambda^2-1)-(\lambda-1)+(1-\lambda) = 0$
$\displaystyle (\lambda)(\lambda^2-1)-(\lambda-1)-(\lambda-1) = 0$
$\displaystyle (\lambda)(\lambda+1)(\lambda-1)-2(\lambda-1) = 0$
$\displaystyle (\lambda-1)[\lambda(\lambda+1) - 2] = 0$
$\displaystyle (\lambda-1)(\lambda^2 + \lambda - 2) = 0$
$\displaystyle (\lambda-1)(\lambda-1)(\lambda+2) = 0$
$\displaystyle (\lambda-1)^2(\lambda+2) = 0$
Don't ask about the cubic equation. You don't want to see it.
Don't ask about the quartic equation. It's even worse.
Really don't ask about the quintic equation. It requires magic darker and eviler than radicals to solve such elusive beasts.
If you must, the secret lies here. But its dangerous to go alone. Take this.