Eigen vaules.

What is K, and what is k? Endomorphisms of vector spaces or (square) matrices have eigenvalues. You're implying that k and K are scalars.

 

Presumably you mean that you have a 2x2 matrix M and working out det(M-kI) yields the quadratic equation


k^2-8k +12 (or possibly k^2-8k-12)

and you want to find the roots of this quadratic equation, or its factorization.

Is that the correct interpretation of what you're saying?

 

Are you saying that the characteristic equation for some linear map is

[tex]k^2 - 8k - 12 = 0[/tex]

and you factored the polynomial as (k-2)(k+3)?

If so, that's incorrect, as you can see by simply multiplying (k-2)(k+3) and seeing that you don't get back your original polynomial.

 

Don't randomly guess and work out the brackets instead. You will see that multiplying by four will do no good. Are you familiar with the ABC formula if so use it.

 

No, then your leading order term would be [tex]4k^2[/tex]

 

Are you aware that not all quadratic equations can be factored in such a neat form? In fact most cannot, this one cannot for -12. It can however for +12, which one are you trying to calculate?

 

Most people would read this as either [itex]k^2-8k-12=0[/itex] or [itex]k^2-8k \pm 12=0[/itex]. The first one, [itex]k^2-8k-12=0[/itex], cannot be factored by using integers. However, [itex]k^2-8k+12=0[/itex] can. Which equation you are trying to solve still isn't clear after 13 posts. And I am not the first one to ask you so please read the posts carefully.

 

Yes you have listed that equation which has a certain inherent ambiguity. I explained this in my previous post. From your last post the equation you're trying to solve is [itex]k^2-8k-12=0[/itex]. This equation cannot be factorized and you will need to use the ABC formula.

 

If you're new to this I really suggest that you use the ABC formula on both [itex]k^2-8k-12=0[/itex] and [itex]k^2-8k+12=0[/itex]. This way you will see how different the answers are.

Secondly factorizing a quadratic equation [itex]k^2+bk+c[/itex] can only be done if you can write it in this form, [itex]k^2+(\alpha+\beta)k+\alpha \beta[/itex], with [itex]b=(\alpha+\beta)[/itex] and [itex]c=\alpha \beta[/itex].